Workshop Blog

Assess-Respond-Instruct: Building Math Readiness

Our conversations in mathematics teaching are often centered around the gaps that we observe in student understanding, or how students are not ready to learn the grade level mathematics that we are trying to teach them. When we look at our teaching practices in other subjects, we know that it is important to Activate and Connect Prior Knowledge, and to provide responsive instruction if there are skills that our students are missing. The same holds true in mathematics, but how do we do this in a structured, systematic and efficient way in our classrooms? The Assess-Respond-Instruct framework, developed with and implemented by teachers from across Saskatchewan, does exactly that.

Foundationally, the Assess-Respond-Instruct framework provides opportunities for

  • teachers and students to know whether students have an understanding and fluency with prior knowledge, and
  • filling gaps in knowledge and build fluency, and
  • engage in grade level mathematics.

In order to embark on this way of teaching, some key questions that drive our planning are:

Differentiation vs Modification

A key idea within mathematics is the difference and similarity between differentiation and modification. Working with a school last week, we brainstormed the following key ideas:

Sometimes, a student needs a modified curriculum because they are unable to grasp mathematical concepts. This determination is made with much consultation with the education team, parents, and students. Communication is key between home and school to ensure that parents understand that their child is not working towards grade level outcomes. Rather, they are on a modified curriculum with modified assessment expectations. When a child is working towards a modified curriculum, it should still be differentiated. Students need to experience a variety of modes and strategies to help them achieve their unique learning goals.

The difficulty is when a student or class is inadvertently experiencing a modified curriculum without the pre-thinking and opportunities to engage in grade level mathematics. This might look like a child being identified as ‘not being able’ to add and subtract in grade 4, so they only work on addition and subtraction when their classmates are working towards multiplication and division. In this example, the child is not given an opportunity to engage in grade level outcomes, so the gap in their learning is even larger the following year.

So what is a possible solution? The Assess-Respond-Instruct Framework!

Designing Pre-Assessments

Pre-assessments should focus on mathematics knowledge that students need in order to be ready to engage in new, grade-level instruction.

Content to Pre-assess

We can identify the pre-skills necessary for a new unit of study by mapping curriculum and asking ourselves “What might students know before this grade to help them understand the content at our grade level?”

For example, in Saskatchewan curriculum Grade 6 Saskatchewan Patterns and Relations

  • P6.1 – Extend understanding of patterns and relations in tables of values and graphs.
  • P6.2 – Extend understanding of preservation of equality concretely, pictorially, physically, and symbolically.
  • P6.3 – Extend understanding of patterns and relationships by using expressions and equations involving variables.

In this Grade 6 Saskatchewan example, the blue concepts are grade-level, while the yellow concepts are mathematical ideas that appear in curriculum before Grade 6. By mapping curriculum, you can see that new, grade-level instruction is only one small step beyond what students have experienced in the past.

Analyzing the pre-skills from the example above, we can see that they can be clustered in the following way:

It is important to identify the extent to which students might need to understand a concept. In this Grade 6 example, students need to understand and be fluent in addition with single digit numbers, and subtraction of double digit minus single digit numbers. We would not usually expect students to work with larger numbers when we are solving algebraic equations at this grade level. Even though curriculum has students learn and practice addition and subtraction to 10,000 in Grade 5, we do not need students to use these large numbers in THIS unit of study, so we would not pre-assess or respond to those large numbers.

The content of a pre-assessment for this example unit of study would include:

  • Addition of single digit numbers and subtraction of numbers no larger than 100.
  • Multiplication of single digit numbers and division of numbers no larger than 100.
  • Representing relations, including tables of values and graphs.
  • Solving one step equations, including balance scale representations and missing value equations.

Forms of Pre-assessments

You might have assessment data that you have gathered through school-system pre-assessments, through tools like Pearson’s Numeracy Nets, or you can develop your own simple Pre-assessments.

How might we respond to gaps in pre-skills?

We need to consider both the content and structure that we are using to respond to gaps in understanding. Many teaching innovations focus on one or the other. I would suggest that we need to consider both the content of intervention as well as the process, or structure, that we use to have students interact with that content.

What is Responsive Content? Differentiating Mathematics Intervention

Too often, our mathematics intervention in upper grades involves symbolic practice of a topic that a student is unsure of. Rather than only focussing on symbolic practice, we need to differentiate our intervention – additional practice worksheets are not enough if a student does not understand.

What does differentiation look like in mathematics? If we consider NCTM’s ways of representing algebraic ideas, and the Theory of Multiple Intelligences, a simple way to look at differentiation for every math concept might be:

Whether we are looking at responsive instruction or new instruction, it is important that students are given opportunities to learn new concepts:

  • Concretely and visually
  • Video – this can help auditory learners watch and listen to math concepts
  • Written explanations – a simple and concise description of that mathematical idea
  • Game – a way to interact with peers and have mathematical conversations
  • Practice – to build fluency with foundational math ideas

A planning organizer is helpful in identifying the components that you will have ready for students who need intervention in each topic. The concepts that we focus on for responsive instruction are those identified in our pre-skill analysis of our next unit of instruction. The modes of responsive instruction need to be thought out for each concept, or skill. This provides a robust framework for intervention.

A Classroom Structure – Responsive Stations

There are many ways to structure your classroom to ensure that your students are receiving the instruction that they need. These might include classroom routines that focus on readiness skills, or rotational stations like Daily 3 Math. One innovative structure is Responsive Stations.

Implementation

Once you have the pre-assessment data, students go to those stations that their data on their pre-assessment indicates that they need.

Some helpful organizational hints include:

  • Colour coding your boards helps students know where they are heading.
  • Use a tracking sheet to monitor which pre-skills each student needs to address.
  • Use stickers as rewards to track what stations have been done.
  • Use a short post-assessment to determine that a student understands the content.
  • Use bins of materials at each station to help keep organized.
  • Include an enrichment station for those students who have pre-skills in place. This enrichment station can include games, additional math topics, and ideas such as creating new videos or games based on math concepts.

Once you have provided opportunities for students to be ready for your grade-level instruction, you can then teach new concepts using rich instructional practices that we know help students understand. Through the year, your class will revisit the same pre-skills over time, as many topics repeat as pre-skills throughout curriculum.

If you are interested in learning more about the Assess-Respond-Instruct Framework for building readiness, or would like to bring professional development to your staff in this area, please contact Terry@johansonconsulting.ca

Teaching Patterns in Early Years

Patterns are everywhere. Exploring and identifying patterns can help children understand our number system, operations, spatial understanding and the foundations of algebra. Mathematics is the study of patterns and exploring them through play can begin mathematical and algebraic thinking in early years. Click here for a downloadable version of this post.

There are several big ideas related to patterns:

  1. Patterns exist and occur regularly in the natural and man-made world.
  2. Patterns can be recognized, extended and generalized using words and symbols.
  3. The same pattern can be found in many different forms – physical objects, sounds, movements and symbols.

The progression of patterns through Saskatchewan Curricula:

When viewing patterns, it is useful to know the following terms:

  • Element – an action, object, sound or symbol that is part of a sequence.
  • Core – the shortest string of elements that repeats.
  • Pattern – a sequence of elements that has a repeating core.

Children will develop their ability to recognize and manipulate patterns differently. Some children will move through the following progression:

Exploring patterns also gives children practice and exposure to other mathematical ideas, including:

  • Counting and cardinality – counting the number of items in the unit of a repeating pattern, or how many items are added in an increasing pattern.
  • Adding and subtracting – generalizing about an increasing or decreasing pattern – how many more or less.
  • Position and spatial properties – which element comes next, which element is between two others, reversing order of elements.

How might you teach patterns?

As with many mathematical ideas in early years, it is important to connect ideas. Learning is not linear! It is important that children use physical materials from their environment to build and explore patterns rather than relying on drawing and colouring patterns. Buttons, toys, linking cubes and natural materials can all be used to create patterns.

The Measured Mom has a list of fun ways to engage young children in exploring patterns. It is fun to take children outside. Megan Zeni describes how you might have children explore Patterns Outside and in Nature.  

Repeating Patterns

Repeating patterns can be introduced using concrete objects, sounds, body movements or symbols. Exploring with a variety of materials can help children identify what is creating a pattern.

Pattern Strips can be made using any shape or object. Students can work independently or in groups to copy the pattern on a strip using real objects. These patterns can then be extended. Watch whether they are copying each element separately or if they have identified the core of the pattern and are able to place all of the elements of the core at the same time. This might look like:

  • If the pattern is red/blue/red/blue – children will place the red and blue at the same time.

A significant step in understanding patterns is when children are able to identify that the same pattern exists even when the materials are different. Using some type of symbol, children are able to code a pattern and compare it to other patterns. If they choose to code the pattern using the alphabet, they might describe it as A-B-A-B or A-A-B-A-A-B. An extension with pattern strips is to create the same pattern with different materials.

Pattern Match can happen in many forms.

  • You can give each group a set of different pattern strips, and they find which strips are showing the same pattern.
  • Children can work in groups, one child is the pattern caller. They choose 3-4 pattern strips and lay them face up on their table. They then ‘secretly’ choose one of the strips and calls out the pattern code. Their group members try to identify which strip is being read.

Growing Patterns

In Saskatchewan, children begin to explore increasing patterns in grade 2, and decreasing patterns starting in grade 3.  The beginning of understanding growing patterns is for children to experience building them with concrete objects.

It is important for children to record their observations. A table can help students record the number for each step in the pattern. Using a table, students can predict how many items are needed to create a certain step in the pattern.

Patterns with Numbers

Number patterns are woven throughout our number system, how we perform operations and the ways we represent numbers. John Van de Walle and LouAnn H. Lovin (Teaching Student-Centered Mathematics K-3, 2006) have created a number pattern activity that has students identify how a number string continues by identifying the pattern present.

Rectangle: Rounded Corners: What’s Next and Why?
Show students five or six numbers from a number pattern. The task for students is to extend the pattern for several more numbers and to explain the rule for generating the pattern. The difficulty of the task depends on the number pattern and the familiarity of students with searching for patterns. Here is a short list of patterns, some easy enough for Kindergarten.
1, 2, 1, 2, 1, 2, …	a simple alternating number scheme
1, 2, 2, 3, 3, 3, …	each digit repeats according to its value
5, 1, 5, 2, 5, 3, …	the courting sequence is interspersed with 5s
2, 4, 6, 8, 10, …	even numbers, skip counting by 2s
1, 2, 4, 5, 7, 8, 10, …	two counts, then skip one
2, 5, 11, 23, ….	double the previous number and add 1
1, 2, 4, 7, 11, 16, ….	the number being added increases by 1
2, 12, 22,32, …	add 10
Most of the preceding examples also have variations you can try. Make your own! (Van de Walle & Lovin, 2006)

Skip Counting

Skip counting is an excellent source of patterns. We often limit skip counting to small numbers like 2, 3 or 5. We also often start skip counting at 0. Children can explore the patterns that are created when we skip count by larger numbers, changing the start number. It is a great idea to use a calculator, so students don’t get bogged down in computation!

  • If we start at 7 and skip count by 5’s, what pattern do we see?
    • 7, 12, 17, 22, 27, 32…
  • If we start at 7 and skip count by 55’s, what pattern do we see?
    • 7, 62, 117, 172, 227, 282, 337, …
  • What do we notice about these two patterns?

Patterns in the Hundreds Chart

Start and Jump on the 100s Chart

Using a hundreds chart, have students colour in the pattern created by one of the Start and Jump Numbers sequences given. If different students represent different patterns, what do they notice?

  • How do patterns change when
    • the start number changes?
    • The jump number changes?
  • Which skip count numbers create columns?

Let’s Build the 100’s Chart

  • Using a pocket 100s chart or interactive 100’s chart. Place the following number cards in the pockets:
    • 4, 10, 17, 32, 48
  • Gather students so they can see the 100’s chart easily.
  • Hold up a number related to one of those in the chart, such as 18. Ask “who would like to place this number?”. Explain how you know where to put it.
  • Choose numbers to place based on the number concepts you are working on:
    • If you are working on adding 10, choose numbers that emphasize that concept.
    • If you are working on skip counting, choose numbers that emphasize what you are counting by.

Game: Arrow Clues

  • Clues can be created on cards or written large enough for all players to play the same clues.
  • Arrow clues can look like:
  • undefined
  • Differentiation:
    • Students can play with or without a 100s chart to refer to.
  • Have students describe the impact of each of the types of arrows on the VALUE of the number.

Missing Number Puzzles

Using the patterns in the 100’s chart, children can figure out the missing numbers when only a part of the 100s chart is provided.

Teaching Place Value

Place value and number sense are foundational concepts on which others build over the years in mathematics. Some of the big ideas within place value include:

Concept Progression Over Time

In Saskatchewan, our curriculum identifies the following ideas:

  • In Kindergarten, children learn that counting tells us how many. The whole numbers are in a particular order and there are patterns in the way we say them that help us remember their order.
  • In Grade 1, children understand place value in individual numbers – they look at 17 as a quantity. We can compare and order numbers.
  • In Grade 2, children understand that the value of the digit depends on its location or place.
  • In Grade 3, children consolidate their understanding that the place determines a number’s value.

Ideas for Teaching Place Value

Rekenreks, 5 and 10 Frames

Number sense is a foundation of place value. Relating numbers to ‘friendly’ 5 and 10 are key ideas that can move children past counting.

Try This – Use a rekenrek to show the following:

  1. Representing numbers – how might children use these tools to represent 7? 3? How do they know?
  2. Quick flash – flash a number of beads on a rekenrek and have children tell you what the number is. How do they know this is the number? Are they counting? Or comparing to the ‘friendly’ 5 or 10?
  3. Model numbers in a number string – showing 4, then 5, then 6. Some children will see the pattern of 1 less than 5, 5, and 1 more than 5. You can then repeat with 3, 5, and 7.

Now try to think through these activities using 5 and 10 Frames and linking cubes to show numbers. How is this the same and different than using a rekenrek? There are a number of games and activities involving dot cards and 10 frames that can emphasize 10.

You can find out more on the Building Math Minds Rekenrek activities site.

Subitizing

Subitizing is a foundational skill and occurs when children know that a number of objects is present without counting. Subitizing can occur with random displays of objects or dots, or patterned dots like you would see on a dice, dominoes or ten frames.

Try ThisBuilding Math Minds has a great site for subitizing games. You can find some ideas in this Evergreen Games Overview.

100s Chart

The hundreds chart is an important tool for children to see patterns in our number system. There are a number of games and activities that you can try to emphasize different math ideas.

Try This – There are a number of blogs and vlogs that teachers have created to highlight the 100’s chart. Buggy and Buddy does a good job curating ideas from a number of sources. You can also have children try to find the missing numbers on a 100’s chart to emphasize the patterns in our number system.

Base 10 Blocks

Based 10 blocks are a foundational manipulative to help children understand our number system.

Try This – Go to Hand2Mind website and scroll down to view the lessons provided. These are organized by grade band so that you can find what might fit your students best. Use the base 10 blocks provided to try to work through some of these lessons

Place Value Misconceptions

Misconceptions can be created by a mis-applied pattern, or incomplete understanding of number concepts. The following are some place value misconceptions that occur in Early Years, and some possible instructional strategies to address them.

Misconception: A number is a number, and does not represent a bundle of 10, 100, 1000 etc. objects regardless of its position in a number.

Example: 1 means one, so when it is placed in a number 17, it still represents one rather than 10.

What to do about it? Use the concrete to abstract continuum to represent 17:

  1. Place value blocks or other counters, such as coffee stir sticks.
  2. Arrow Cards
  3. Find the digit on the 100’s chart

Misconception: Students represent numbers after 100 as they sound.

Example: Students think that the number after 100 is 1001, then 1002, 1003, etc.

What to do about it: Use a chart that goes beyond 100, have children fill in the next numbers after 100.

Misconception: The student orders numbers based on the value of the digits, instead of place value.

Example: 67>103 because 6 and 7 are bigger than 1 and 2.

What to do about it: Have students represent numbers using base 10 blocks and then write out expressions using > and < when comparing.

What to do about it: Have students show numbers on a number line to see which numbers are further from zero to the right.

Misconception: The student struggles with the teen numbers, as they are different from the pattern in other decades.

Example: Students may say “eleventeen” or may not understand that 16 is ten and six. They may also think that sixteen is 61 because we say the number six first.

What to do about it: Christina, The Recovering Traditionalist, has curated a number of games and ideas for addressing how to teach the teens.

Having Fun with Math

Mathematics should be playful, and there are a number of games that can build fluency in mathematics.

Combo-10

This game allows students to see how numbers fit together to make 10 using domino-like game pieces. It is for groups of 2 – 4 players.

Try This – Play with at least two people or groups. Each group needs 1 set of dominoes. Lay them face down. Each person/group draws 7. The rest are the draw pile.

  • The player with the highest double (or most dots if there are no doubles drawn) plays first. A piece can be played if the number of dots on one side of the domino adds to 10 with a domino on the table. Doubles can be laid sideways, allowing more arms to grow.
  • A wild card is a domino whose dots add to 10. If you play a wild card, you can play twice.

Snap

Snap is a game played with linking cubes. Each pair receives 10 linking cubes. Players may want to start with the cubes in a stack, alternating colours:

Try This – One player has a stack of 10 cubes behind their back. ‘Snap off’ part of the stack and show the part that is remaining to your partner.

The partner tries to guess how many were snapped off and hidden from view. The unknown part is revealed.

Variations:

  • Using more or fewer blocks in the stack.
  • Breaking the 10 cubes apart and hiding some of them underneath an opaque glass or container.

Race to 100

The goal of this game is to get to 100 first without going over.

Try This – Play the Game

Each player starts at 1. The first player uses a spinner or dice to generate a number. They can move up the 100s chart by their number of tens or ones until one player gets to 100 without going first.

Variations:

  • Each player gets 6 turns. The closest to 100 without going over wins.
  • Continue playing until a player lands exactly on 100. If the roll takes them over 100, they lose that turn.

Math Swat

Adapted from https://kidsactivitiesblog.com/

cool math game

Flyswatter math combines the fun of moving and slapping with the chance to learn number recognition and solving math problems.

Creating the game board: The game board can be as small or as large as you would like and include the number range and type of numbers that you are working with in your classroom.

Try This – Play a Game with two lines of players. Each line has their own swatter.

  • Counting: swat the numbers in order – in either direction.
  • Number recognition: say the number and have learners swat the correct symbol.
  • Counting and 1:1 correspondence: give a number of counters, blocks, etc – they count and then swat the number.
  • Addition or subtraction facts: give the fact, swat the correct sum.
  • Addition facts: give the sum and one addend, swat the missing part.
  • Skip counting: swat the numbers as they count by 2s, 5s, etc.

Using Technology in Mathematics

Technology can be used to enhance mathematics in a number of different ways:

Place Value Online Games

As you know, not all online games are created equally! Sometimes, they are just online worksheet with little engagement. Sheppard Software is a site that encourage practice through play, including flexible thinking about place value.

Try This – Try playing one of the place value games, Underline Digit Value, on Sheppard Software.

Interactive Whiteboards

These whiteboards all allow you and students to share thinking. They can include audio, pictures, and mark ups. Some apps are free, while others require a subscription.

Try This – Log into one of the interactive whiteboards below that you have not used before. Use the username and password provided on the sticky note!

Interactive Manipulatives  – ICT Math

These interactive manipulatives can be used to explore math ideas. These tools are web-based and do not require a log in or download.

Try This – Go to the Arrow Cards tool in the “Teaching Tools” at ICT Math. You can show the value of numbers using arrow cards along with either rek-n-reks or base 10 blocks simultaneously. Show the value for 3299. What happens when you add one more ones digit?

QR Code Scavenger Hunt

This teaching idea comes from Kristin Kennedy and is available free on Teachers Pay Teachers. It would be relatively easy to create your own based on this idea.

Planning for Outcomes-Based Assessment

Outcomes-Based Assessment (OBA) has been on our educator radar for years. I have the pleasure of working with groups of teachers throughout Saskatchewan to dig into what we know, what we wonder about and examine logistical barriers or problems to solve in order to move forward.

What do teachers know? What do teachers wonder about?

Used to Know I ThinkProfessional development needs to surface teacher knowledge, including any misconceptions that might exist. Too often, professional learning facilitators assume that educators do not know anything so begin from the beginning… or assume that educators know everything and are choosing to resist change. I would argue teachers know a lot… and they, as a collective, want to do best for students and learning. Just like in a classroom, misconstruction of knowledge can occur. It is our job as learning facilitators to use our formative assessment skills to expose understanding and misunderstanding so that we know what to do next.

When teachers are asked, What do you know about Outcomes-Based Assessment? Their answers might be similar to those generated in NLSD:

Know Complete

It is important when broad statements are made that they are clarified by the group.

  • Clarification may be needed on the term ‘learning behaviours’. These include things like attendance, behaviour, neatness, compliance with assignment expectations. Schools or systems may have other ways to communicate these ‘Hidden Curriculum’ expectations to students and parents outside of their academic achievement scores.
  • Clarification may be needed around the idea that assessment is based on “where they are at right now… can change over time”. An example where a student shows competency later in the year after that unit of study has been completed. This may raise some logistical questions around how this would work within a student information system or what impact this idea has on reporting. Once specific questions or logistical barriers surface, it is possible for a school or system to determine procedures so that they can have consistency.

As Tomas Guskey states, there is NO best practice in grading. There are ‘better’ practices that we want to embrace, but there is no universal, standardized and mechanical way to generate a grade for our students.  This was an empowering point with teachers to know that their professional judgment, based on an understanding of curricular outcomes and observable student behaviours, is the most important assessment practice. 

question mark

Along with what educators know, it is vital that we surface what they wonder about. Questions can frame teachers’ professional inquiry for a day of learning, as well as indicate what they need to be emphasized within the agenda. Typical questions around this topic may be:

  • How do I translate an outcomes-based assessment rubric into a %?
  • How do we gather, translate and score observations and conversations so that they ‘count’ like products?
  • What might a teacher daybook/unit plan look like using outcomes-based assessment?
  • Is all assessment outcome-based assessment?
  • What do we do if an assignment is late or not handed in?
  • What is the minimum/maximum number of indicators that we need to assess in order to maintain the integrity of the outcome?
  • How do we use outcome-based assessment in cross-curricular teaching?

It is important that participants choose which question(s) they are most invested in to solve, and provided time within a professional learning experience to discuss possible solutions with colleagues.

Assessment practices are founded on both beliefs and knowledge. A Talking Points Strategy can help to have small groups explore and surface their beliefs about assessment.

Starting with Curriculum

Learning targets are based on curricular outcomes. There are a number of different unit and lesson planning templates used in education. One useful process is to use a thinking map. This graphic organizer allows us to see the connections amongst curricular outcomes, instructional activities and assessment criteria.

Unpacking Outcomes

Starting in the centre, teachers can identify the connections between the nouns (concepts) and verbs (observable behaviours) of the curriculum with the activities that allow students to show those behaviours. The assessment criteria should be related to the curriculum rather than the activity.

For example, in Saskatchewan Science 10, one part of the SCI10-CD1 Outcome: Assess the implications of human actions on the local and global climate and the sustainability of ecosystems. Some of the indicators related to this outcome might be addressed in the following progression:

Outcome Unpacking

By unpacking into a circular thinking map, it is possible to see how the concepts and observable behaviours work together. This will lead to a holistic view of curriculum that eradicates the question of how many indicators are important to address.

Principles of Assessment

Rick Stiggins has developed a set of key ideas related to classroom assessment:

Stiggins Principles

(Chapuis, Commodore, Stiggins, 2016)

From Criteria to Rubrics

There are a variety of assessment tools, including checklists, portfolios, and rubrics. They all rely on clear learning targets or criteria for student success. What does success look like? What are we looking for?

Criteria Statements

Expanding on clear learning targets, Sue Brookhart shares some of her ideas on building high-quality rubrics.

Description Statements

Rubric Pitfalls

Sue Brookhart’s ideas have been incorporated into this simple editable Rubric Worksheet.

Used to Know I Think 3

Formative and Summative Assessment

Too often, formative assessment is defined as ‘things that are not marked’, while summative assessment is defined as “things that are graded at the end of a unit”. This implies that learners can only show understanding that ‘counts’ at the end of a unit of study. So what happens to all of their thinking, work and brilliance along the way? Is it possible that a learning and assessment experience might be both or either for different students? Is it possible that formative and summative assessment are interconnected?

Definitions

One definition for assessment is the ways in which instructors gather data about their teaching and students’ learning (Northern Illinois University, Faculty Development and Instructional Design Center). This definition implies that assessment’s purpose is multi-faceted – to inform students and teachers regarding student understanding as well as to inform teachers about their practice in teaching. Assessment, whether it is formative or summative, is a snap-shot in time that changes with instruction and understanding.

Used to Know I Think 1

Formative Assessment

In his book, Embedding Formative Assessment, Dylan Wiliam defines Formative Assessment as:

“An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have made in the absence of that evidence” (Wiliam, 2011).

This definition implies:

  • Formative describes the function of the assessment rather than the form.
  • Teachers, students and peers might be involved in deciding how to respond to assessment information.
  • There must be a responsive action based on the data in order for the assessment to be formative. Responsive actions are instructional in nature.

If formative assessments are designed with no clear decision/action implied, then the assessment is not useful. The five key strategies for improving student achievement through formative assessment are:

Who Where the learner is going Where the learner is now How to get there
Teacher 1. Clarifying, sharing and understanding learning intentions and criteria for success. 2. Engineering effective classroom discussions, activities, and tasks that elicit evidence of learning. 3. Providing feedback that moves learning forward.
Peer 4. Activating learners as instructional resources for each other.
Learner 5. Activating learners as owners of their own learning.

(Wiliam, 2011, p. 46)

Summative Assessment

Summative assessment is often described as providing information about or evaluating the attainment of understanding or achievement compared to a standard. Katie White (Softening the Edges, 2017) has created a holistic view of summative assessment as part of a larger assessment cycle.

“We engage in formative assessment, feedback and self-assessment regularly. Only after all this do we verify proficiency with summative assessment. It is at this point that we make professional judgments about whether to re-enter the learning cycle because proficiency has not yet been reached or to transition into enrichment or the next learning goal… Viewing summative assessment as part of a larger continuous cycle frees us to make decisions that are right for our learners and right for ourselves” (White, 2017, p. 139).

Formative Summative Cycle

(The Learning and Assessment Experience at UNSW)

The goal of summative assessment is to evaluate student learning. When viewed as part of a cycle, we can see that an assessment intended to be summative may, in fact, become formative. Similarly, there may be times that an assessment intended to be formative might become summative if a learner is able to show proficiency during that experience.

If we view the terms formative and summative as how the assessment is used rather than the tool or the intent for use, it can help us to see all experiences as part of a larger assessment plan.

Used to Know I Think 2

Brookhart, S. (2013). How to Create and Use Rubrics for Formative Assessment and Grading. Alexandria: ASCD.

Chappuis, S. J., Commodore, D. C., & Stiggins, R. J. (2016). Balanced Assessment Systems: Leadership, Quality and the Role of Classroom Assessment. Thousand Oaks: Corwin.

Guskey, T. R. (2019, February 28). Let’s Give Up The Search for ‘Best Practices’ in Grading. Retrieved from Thomas R. Guskey & Associates: http://tguskey.com/lets-give-up-the-search-for-best-practices-in-grading/

UNSW Sydney. (n.d.). Guide to Assessment. Retrieved March 12, 2019, from UNSW Student Home: https://student.unsw.edu.au/assessments

White, K. (2017). Softening the Edges. Bloomington: Solution Tree.

Wiliam, D. (2011). Embedded formative assessment. Bloomington, Indiana, United States of America: Solution Tree Press.

 

 

 

Math Instruction for ALL Students

This blog post is a work in progress! Be sure to come back and visit in a few weeks, as I will be adding to it over time…

It can sometimes feel overwhelming when we look at all of the individual and group needs of our mathematics learners. Building readiness to learn, along with ensuring that we meet the individual needs of students might give us the impression that we need to create an individual lesson plan for each and every person in our classrooms. That sounds exhausting…

But what if we can create structures and use a variety of math instructional strategies within those structures? What if we can create diverse learning experiences that encourage mathematical thinking and growth over key concepts? This is an idea worth investigating!

I am still learning

Our elementary and middle years math curricula in Saskatchewan cover a number of topics, from number to patterns to shape and space and statistics. Ironically, when you look at the skills needed for students to be READY to engage in these grade-level concepts, there are only a handful of pre-skills. These pre-skills are the math concepts that are applied and used in new learning.

For example, when we are learning about adding and subtracting fractions, we need to know about:

  • addition and subtraction
  • multiplication and division, multiples and factors
  • what a fraction is, finding equivalent fractions, improper fractions

When you analyze grade-level outcomes in mathematics, you will often see combinations of the following pr-skills:

  1. Number Sense and Place Value
  2. Addition and Subtraction
  3. Multiplication and Division
  4. Parts of a Whole – Fractions, Decimals and Percent
  5. Algebraic Thinking

So, how do we teach and reteach each of these key concepts in our classrooms? You can find a large number of curated resources in this Google Drive: https://bit.ly/2zrNfqd which contains folders of resources designed to help you to teach through these continuums, as well as:

  • What is an instructional sequence and strategies for teaching each concept?
  • What are some common misconceptions and how might we address them?
  • How might we infuse technology into our mathematics instruction?
  • What are some fun ways to engage in mathematics?
  • How might we use math with a purpose to gain a deeper understanding of social issues?

Concept Continuums

When we look at our Saskatchewan curriculum, we can see how concepts grow over time in these math Curricular Through Lines:

We can also pull out specific concepts and see how they grow. The following concept trajectories were created by a province-wide math leadership group a number of years ago, and show the language, strategies and concepts over time. Each continuum has four instructional strategies listed.

The Circle of Courage: Building Resilience

In their book, Reclaiming Youth at Risk, Brendtro, Brokenleg and Van Bockern (1990) proposed a model of youth empowerment and resiliency. This model is called the Circle of Courage, and it is based on research of First Nations philosophy of child rearing. The Circle of Courage is a holistic approach that is described by Dr. Martin Brokenleg in his video.

Dr. Brokenleg’s research shows that every human being has four basic needs: significance, competence, power and virtue. The Circle of Courage makes the following connections:

 

Circle of Courage Stems

Dr. Brokenleg has identified what it looks like in someone whose spirit is in a state of weakness, a state of strength, and what might happen if their spirit has been distorted. The following are ideas to support a state of strength by helping to mend a broken spirit.

Circle of Courage Graphic

Belonging: Right now, I belong here.

Belonging is our most basic need. Maslow’s hierarchy (McLeod, 2018) recognizes that a child needs to belong before they can move towards building self-confidence and self-actualization (Peterson & Taylor, 2009). maslow-5To feel that we belong, we must build relationships with others. Complex kinship systems have existed within First Nations communities for thousands of years (Learn Alberta, 2019). By building a sense of kinship within your classroom, you can ensure that students feel a sense of belonging, culturally socially and physically.

Weak Spirit of Belonging Distorted Spirit of Belonging

Spirit of Belonging

Distrust Overly Dependent Trust
Exclusion Cult Vulnerable Inclusion
Detachment Gang Loyalty Warmth
Rejection Craves Acceptance Friendship
Antagonism Craves Affection Cooperation

To build a sense of belonging, create physical spaces for all. The arrangement of the classroom should reflect the need to serve whole group, small group and individual work needs through:

  • Desk arrangements
  • How large furniture allow for student movement
  • If possible, have a quiet space for those who need it

Include all students in time to learn together. Have all students of different abilities, ethnicities and backgrounds working in the same classroom. They can cooperate, communicate and care for one another. By engaging in heterogeneous groupings frequently, students can know one another deeply. Assistive technologies can help to support students who have mild or severe disabilities and help them to contribute the learning of the whole.

Provide opportunities for students to know each other, such as an Interview and Share activity. Provide positive encouragement to try new activities and recognize individuality and creative talents.

Mastery: I may not be perfect at everything, but I will always try to get better.

Mastery is not only of the cognitive domain, but it is also a holistic view of learning that includes physical, social and spiritual competencies. Giving children the opportunity to develop all parts of self can help to grow a strong spirit of mastery.

Weak Spirit of Mastery

Distorted Spirit of Mastery

Spirit of Mastery

Failure Oriented Arrogant Successful
Unmotivated Workaholic Motivated
Non-Achiever Over Achiever Achiever
Avoids Risks Risk Seeker Creative
Fears Challenges Cheater Problem Solver

To build a sense of mastery, teach students using authentic, relevant, differentiated learning. This includes things such as low floor, high ceiling tasks, open-ended and parallel tasks, and being cognizant of multiple intelligences when planning instruction and assessment.

Using Outcomes-based assessment and tracking progress towards a set standard can help students and teachers know where learning is at and respond accordingly. Dylan Wiliam has identified that clarifying learning targets is key to improving achievement and mastery (2011). When the criteria for success is visible and understood, students can strive for it. Teaching students to set learning goals and solve problems through collaboration can help them to build a spirit of mastery. Communicate teacher expectations clearly and provide specific feedback on student behaviour.

Independence – Earning independence by building trust.

One of the goals of education is for students to own their own learning. Dylan Wiliam (2011) has identified that goal setting and strategies for students to direct their learning path and destination. It is important that if students are pulled out of the classroom for additional support, they understand that it is to help them become independent when they rejoin their classmates. Student empowerment is important to build intrinsic motivation and confidence to persist through learning experiences.

Weak Spirit of  Independence Distorted Spirit of Independence

Spirit of Independence

Impotent Manipulative Powerful
Coerced Dictatorial Assertive
Unassured Defies Authority Confident
Misled Rebellious Self-Control
Futility Reckless Optimism

Building a democratic classroom can occur through classroom meetings to make decisions, offering choices within curriculum, and co-constructing classroom rules and norms. This can be done through the Circle of Courage itself, with groups brainstorming what it looks like when we work together to build a sense of belonging, mastery, independence and generosity within our community of learners.

By teaching self-regulation, we encourage and build independence and self-control. This can assist students in maintaining focus and personal responsibility.

Generosity – Giving to others makes you feel good.

The virtue of generosity is one of the most valued within Indigenous communities. There is a responsibility to care for others within our community. By being generous, learners can develop a sense of pride and joy. Service projects and creating spaces that allow for generosity to occur can help to strengthen students’ spirit of generosity.

Weak Spirit of Generosity Distorted Spirit of Generosity

Spirit of Generosity

Emptiness Driven Purpose
Rancour Over Involvement Empathy
Exploiting Servitude Kindness
Vengeance Co-Dependent Forgiving
Disrespectful Plays Martyr Respectful

Citizenship education can help us to build a caring community within and outside of our classrooms. At the beginning of the school year, create opportunities for students to know each others’ stories. Activities such as collaborative writing, field trips together, assigned student jobs contributing to the well being of the class, and collaborative problem-solving activities can help students experience giving and receiving support. By watching slide shows of classmates completing tasks can all build a sense of care.

Introducing and teaching the Circle of Courage can help your students understand how they are building their own and their classmate’s resilience and spirit.

Brendtro, L., Brokenleg, M., & Van Bockern, S. (1990). Circle of Courage. Retrieved February 14, 2014, from Reclaiming youth international: http://www.reclaiming.com/content/aboutcircleofcourage

Circle of Courage Model – Spaces. (n.d.). Retrieved 05 15, 2019, from Portland Community College: https://spaces.pcc.edu/download/attachments/13337564/Circle+of+Courage+Model.doc

Learn Alberta. (2019). Kinship. Retrieved May 8, 2019, from Walking Together: First Nations, Metis and Inuit Perspectives in Curriculum: http://www.learnalberta.ca/content/aswt/kinship/

McLeod, S. (2018). Maslow’s Hierarchy of Needs. Retrieved May 5, 2019, from Simply Psychology: https://www.simplypsychology.org/maslow.html

Peterson, J. M., & Taylor, P. D. (2009). Whole Schooling and the Circle of Courage. Retrieved May 8, 2019, from Whole Schooling Consortium: http://www.wholeschooling.net/

Discipline with Dignity: Trauma-Informed Classroom Management

Classroom management is the part of teaching that is invisible when it is working well, and highly visible when we and our students are struggling. Sometimes it may feel like herding cats:

Classroom Management’s purpose is to “provide structure while helping students develop autonomy, awareness and self-regulation skills” (Emerich France, 2018).

Traditional classroom management theories rely on teachers viewing student behaviour as a matter of choices or intentional defiance. As a result, traditional solutions have been a list of consequences and rewards. While consequences may be a part of a classroom management plan, if the goal of classroom management is to have students understand themselves and self-regulate, teachers and students need to first identify the causes of behaviours, attempt to prevent triggers and increase self-awareness.

General principles of Discipline with Dignity (Curwin, Mendler, & Mendler, 2018) are:

General Principles

This perspective of classroom management allows us to link the effects of trauma and brain development to understanding some of the underlying causes of student behaviours. Classroom management is founded on knowing our students and building relationships with them.

Basic Needs that Drive Behaviour

Curwin, Mendler, and Mendler (2018) and Dr. Martin Brokenleg (Circle of courage, 1990) have identified what our and our students’ basic human needs are in order to be healthy and whole.

Curwin, Mendler, and Mendler Dr. Martin Brokenleg
Identity – “how we view ourselves and how we feel about ourselves”
Attention – “the need to be acknowledged by others in a way that makes us feel that we matter” Generosity – to give our knowledge, skills, insight, experience, and resources to others; receiving a sense of purpose from strengthening the community
Connection – “our need to feel that we belong to something that matters to us” Belonging – to feel valued, affirmed and significant within the group; believing in the importance of a shared purpose; to identify with shared goals
Competence – “feeling that we know how to do something” Mastery – to develop abilities, skills, and knowledge in order to take risks, to try new things and learn from others; to embrace challenges and learning
Control – “the desire to make decisions that count, to have real choices, to control our environment” Independence – to feel in control of our learning; to have a sense of competent autonomy and to contribute to responsibility

Saskatchewan teachers and educational assistants used a Circle of Courage graphic organizer to brainstorm what they need to keep in mind to create a learning environment that fosters a sense of belonging, mastery, independence, and generosity in their students:

Circle of Courage

A school environment that provides opportunities for students to have their needs met is part of a “prevention mindset” (Curwin, Mendler, & Mendler, p. 61). Looking at prevention from the student perspective, appropriate behaviour is generally achieved when students:

  • Feel connected to the teacher, one another, and the curriculum.
  • Believe that success is attainable with reasonable effort.
  • Feel respected by being heard; feel teachers strongly care about them in personal ways.
  • Are given responsibility, especially in helping other children. This involves giving appropriate choices throughout the day.
  • Look forward to sanctioned moments of joy and laughter every day.
  • Believe that what is being taught is relevant.

Activating Peers as Learning Resources

Dylan Wiliam has identified five strategies for Formative Assessment, which increase student engagement and achievement. Formative Assessment Strategies

Wiliam’s work guides our instruction in many ways, including how to activate learners as instructional resources. Collaborative learning that encourages group goals and individual accountability is more powerful than simply having students work on tasks in a group. This group work increases student sense of belonging and provides a space for generosity within a community of learners.

Cooperative Learning

Wiliam (2011) identifies why students benefit from helping their peers:

  • they are working towards a common goal and they benefit from the efforts of all, resulting in increased motivation.
  • they care about their group members, resulting in social cohesion.
  • they understand and can address the difficulties their peers are having, resulting in personalization.
  • thinking together brings clarity, resulting in cognitive elaboration.

Assessment Strategies

Wiliam writes about a number of strategies that can enhance peer support of learning within a classroom.

Peer Support Strategies

In his book Embedding Formative Assessment, Wiliam suggests many strategies, including:

  • Peer Evaluation of Homework – The class or teacher create criteria (rubric) for the work. Who is assessing the work changes and is not announced until the homework is complete. Evaluators may be: Self, Other – individual or group or Teacher
  • Two Stars and a Wish – student feedback on other students’ work – 2 positive qualities and a suggestion for improvement; Teacher needs to instruct students on what quality feedback looks like. Sentence starters can be useful to give to students in advance.
  • Preflight Checklist – When there are specific requirements or features of a piece of student work, this list is checked by a peer prior to the work being handed in. If there are pieces missing that were on the checklist, the peer is the one held accountable.
  • Group-Based Test Prep – Within a group, each student is assigned a different part of a unit to review. They prepare and present their review to their group. Peers assess the review using coloured cups (red – not as good as I would have done; yellow – about the same as I would have done; green – better than I would have done).

Teaching and using group work goes beyond learning styles, and can enhance student motivation, engagement and resilience.

Stress Behaviours

(Adapted from The Mehrit Centre’s Infographic on Understanding Stress Behaviour for Teachers)

Brain research has shown that there are differences between stress behaviours and misbehaviour. If we treat them in the same way, it can be hard on our students and hard on ourselves.

Stress Behaviour

The 5 Primary Domains of Stress

There are many different reasons why a student might show signs of stress behaviour. These are linked to Shanker’s five domains of self-regulation.

5 Domains of Self-Reg

Signs of Stress Behaviour

Stress behaviours (Shanker, 2018) are biological in nature and neither intentional nor conscious choices on the part of students. These might include:

  1. Heightened impulsivity
  2. Difficulty ignoring distractions
  3. Problems in mood (sees everything negatively)
  4. Erratic mood swings
  5. Trouble listening
  6. What she is saying doesn’t make sense

Dealing with Stress Behaviour in Students

When a child exhibits stress behaviour, what do we do as educators? Shanker (2018) suggests that we:

Dealing with Stress

Along with specific calming strategies that can help students, include mindfulness strategies and ways to integrate social-emotional learning throughout the day.

Effects of Early Trauma

“Trauma has a powerful capacity to shape a child’s physical, emotional, and intellectual development, especially when the trauma is experienced in early life” (JBS International and Georgetown University National Technical Assistance Centre).

Three Types of ACEs (Adverse Childhood Experiences)

ACEs

There are significant impacts of ACEs on individual health outcomes. Brain science has determined that ACEs disrupt neurodevelopment, which leads to social, emotional and cognitive impairment, adoption of health-risk behaviours, disease, disability, and social problems and eventually can lead to early death.

Adverse-Childhood-Experiences-1-logo.png

Continued exposure to trauma creates an environment filled with relentless fear, resulting in the development of a self-defence mechanism in a child’s brain that requires a fight, flight or freeze response. Stress responses are maintained due to:

  • A persistent fear response that ‘wears out’ neural pathways;
  • Hyperarousal that causes children to overreact to non-threatening triggers;
  • Dissociation from the traumatic event in which the child shuts down emotionally; and
  • Disruptions in emotional attachment, which can be detrimental to learning.

(JBS International and Georgetown University National Technical Assistance Centre).

Intergenerational and Historical Trauma

The Georgetown University National Technical Assistance Centre for Children’s Mental Health has identified two types of trauma that may have an impact on children in schools:

  • Intergenerational trauma results when disturbing experiences have not been addressed and their emotional and behavioural legacy is passed down from parents to their children. Parents who experienced persistent trauma in childhood may struggle with their own ability to express empathy, compassion, and self-regulation. Unresolved trauma may make it difficult for parents to build trusting relationships and healthy attachments. This trauma is then transmitted to future generations.
  • Historical trauma goes beyond a single family to a community caused by historical, systematic abuse and injustice. In additional to family-specific intergenerational trauma, historical trauma may also result in shame and loss of culture and identity. The legacy of historical trauma can result in “repression, dissociation, denial, alcoholism, depression, doubt, helplessness, and devaluation of self and culture”.

Brain Malleability

While trauma affects brain development, causing structural and hormonal changes, the malleability of the human brain brings us hope. Because the brain can heal, and new neuropathways can be developed, teachers and schools can impact the long-term social, emotional and physical impacts of trauma. Trauma-informed schools are those where the school climate, instructional designs, positive behavioural supports, and policies are created so that traumatized students have what they need to achieve academic and social competence (Craig, 2016).

PBIS – Positive Behavioural Interventions and Supports SEL – Social Emotional Learning
The goal of PBIS is to create a positive school climate, in which students learn and grow. A process through which children and adults acquire and effectively apply the knowledge, attitudes, and skills necessary to understand and manage emotions, set and achieve positive goals, feel and show empathy for others, establish and maintain positive relationships, and make responsible decisions.

Dr. Bruce Perry has done significant research in the area of mitigating the impact of trauma on children.

Dr. Perry contributes to the Child Trauma Academy, which makes a number of free resources available.

Solutions in classrooms directed at brain stem activity can help create new pathways in the brain’s cortical areas. These include

  • patterned rhythmic activities
  • walking
  • dancing
  • singing
  • meditative breathing
  • create a calmer cognitive state so higher order thinking can occur
  • scaffold new information on prior knowledge
  • use classroom discourse purposefully
  • peer collaboration
  • provide direct instruction

Instruction and school environments that provide calming opportunities can help children learn to be more self-aware and foster their own emotion regulation, which then impacts the behaviour-consequence cycle.

As teachers, when we understand the underlying causes of student behaviour, we can not only respond, we can avoid triggers. Classroom Management is more than just the strategies we use, it is the relationship and understanding of the children we teach in order to help children build new neural pathways, understand their own behaviour and learn to self-regulate.

When and Where to Refer Students?

Sometimes, we might recognize that one of our students requires additional supports. Central Office personnel or support teachers may be able to help you assess where your students are at. For parents, Amy Morin writes about some of the indicators that a child might require targetted services in her blog post “When Should Parents Seek Help for a Child’s Behavior Problems?”. Supports from outside of your school system may be available through your regional health authority, which is listed on the Saskatchewan Health Authority’s Website. In the Prairie North Health Region, for instance, there are a number of youth-focussed supports in North Battleford.

Works Cited

Brendtro, L., Brokenleg, M., & Van Bockern, S. (1990). Circle of courage. Retrieved February 14, 2014, from Reclaiming youth international: http://www.reclaiming.com/content/aboutcircleofcourage

Craig, S. E. (2016). Trauma-Sensitive Schools: Learning Communities Transforming Student Lives K-5. New York: Teachers College Press.

Curwin, R. L., Mendler, A. N., & Mendler, B. D. (2018). Discipline with Dignity: How to Build Responsibility, Relationships, and Respect in Your Classroom. Alexandria: ASCD.

Emerich France, P. (2018, September). A Healthy Ecosystem for Classroom Management. Educational Leadership, 76(1). Retrieved from http://www.ascd.org/publications/educational-leadership/sept18/vol76/num01/A-Healthy-Ecosystem-for-Classroom-Management.aspx

JBS International and Georgetown University National Technical Assistance Centre. (n.d.). Issue Brief 1: Understanding the Impact of Trauma. Retrieved from https://gucchdtacenter.georgetown.edu/TraumaInformedCare/issueBrief1_UnderstandingImpactTrauma.pdf

Shanker, S. (2018). (The MEHRIT Centre) Retrieved August 18, 2018, from Shanker Self-Reg: https://self-reg.ca/

Sousa, D. A. (2009). How the Brain Influences Behaviour: Management Strategies for Every Classroom. Thousand Oaks: Corwin Press.

Wiliam, D. (2011). Embedded Formative Assessment. Bloomington, Indiana, United States of America: Solution Tree Press.

Comprehension Across Subjects

Comprehension strategies are ways in which we make meaning of the information we take in through text, media, and sound. Often considered the domain of the English Language Arts teacher, we now realize that it is important that teachers across subject areas and grades encourage meaning making and use tactics that cause learners to use strategies that they may or may not be fluent in.

Depending on which researcher you follow, you may categorize comprehension strategies into 6, 7, or even 13 different strategies. Following the framework of Ellin Keene (1997) in her book Mosaic of Thought: Teaching Comprehension in a Readers Workshop, this post identifies seven strategies that help learners make meaning of complex information. A detailed comprehension strategies summary describes the actions of readers, writers, mathematicians, and researchers.

comprehension dog
Photo by Jesse757 – Creative Commons Attribution License  https://www.flickr.com/photos/7721141@N07

While categorizing strategies and tactics is helpful, we need to keep in mind that the comprehension strategies are all interconnected. Visualization is grounded on activating and connecting knowledge. Determining importance and summarizing are closely related. Monitoring comprehension often creates self-questions. Each person has different comprehension strategies that their mind tends to use. Our challenge as teachers is to create a pause and opportunity for students to try stretching to new mental pathways.

Activating and Connecting Prior Knowledge

This comprehension strategy involves students connecting their learning to past experiences, events in the world, and to other learning they may have in and out of school. We simply can’t understand new information that we hear, read or view without thinking about what we already know. It is important that teachers teach learners to:

  • Relate to prior experience.
  • Make connections between text, media, and personal observation.
  • Connect the new to the known – use what learners know to understand new information.

visual dictionary - activating and connectingWhen students are using this comprehension strategy, you may hear them say…

  • This reminds me of…
  • I noticed…
  • It made me think of…
  • I never knew…
  • That changed my mind…
  • This is different from…

Some tactics that teachers might use to promote activating and connecting prior knowledge include:

Monitoring Comprehension

This comprehension strategy involves students recognizing and acting on their own confusion, and their self-questioning to determine understanding. We monitor our comprehension and keep track of our thinking in a number of ways. We notice when text makes sense and when it doesn’t. We ask questions, infer, activate background knowledge, and make connections, all in the effort to promote understanding. It is important that teachers teach learners to:

  • Become aware of their thinking as they read.
  • Notice when meaning breaks down and their mind wanders.
  • Employ ‘fix up’ strategies – reread for clarification, read ahead to construct meaning, use context to break down unfamiliar words, skip difficult parts and continue to see if meaning becomes clear, check and recheck answers and thinking, and examine the evidence.

visual dictionary - monitoring comprehensionWhen students are using this comprehension strategy, you may hear them say…

  • I think…
  • I understand…
  • This doesn’t make sense…
  • Oh, now I get it…
  • A part I had trouble with…

Some tactics that teachers might use to promote monitoring comprehension include:

Asking Questions

This strategy involves students actively wondering about topics and questioning facts and information. Questioning is the strategy that propels learners on and is at the heart of inquiry-based learning. Humans are driven to make sense of the world, and questions open the doors to understanding. It is important that teachers teach learners to:

  • Wonder about the content, concepts, outcomes, and genre of text.
  • Question the author.
  • Read to discover answers and gain information.

visual dictionary - asking questionsWhen students use this comprehension strategy, you may hear them say…

  • I wonder…
  • I’m curious…
  • My big question is…
  • Why…
  • Do you know anything about…

Some tactics that teachers might use to promote questioning include:

Making Inferences

This comprehension strategy involves students predicting, hypothesizing, interpreting, and making conclusions. Inferential thinking allows learners to grasp the deeper essence of text and information. Readers infer by taking their background knowledge and merge it with clues int he text to draw a conclusion or arrive at a big idea that is not explicitly stated in the text. It is important that teachers teach learners to:

  • Use context clues to figure out meaning of unfamiliar words.
  • Draw conclusions from evidence.
  • Predict outcomes, events and observations.

visual dictionary - making inferencesWhen students use this comprehension strategy, you may hear them say…

  • I’m thinking…
  • It seems to me…
  • I’m guessing that…
  • I predict…
  • Probably…

Some tactics that teachers might use to promote inferring include:

Determining Importance

This comprehension strategy involves students evaluating information, making judgments about information, and identifying key ideas and concepts. We read nonfiction to learn, understand, and remember information. It is important that teachers teach learners to:

  • Target key information.
  • Choose what to remember.
  • Construct big ideas from smaller ideas.

visual dictionary - determining importanceWhen students use this comprehension strategy, you may hear them say…

  • This is really important…
  • The most important ideas here are…
  • So far, I have learned that…
  • I think this part means…

Some tactics that teachers might use to promote determining importance include:

Visualizing

This comprehension strategy involves students making mental pictures and/or mind maps of ideas and how they interconnect. Visualization builds complex connections and involves more than just how something looks. It extends to other senses such as smell, touch, sound, and taste. It is important that teachers teach learners to:

  • Gain information from the images they construct and view.
  • Create mental images drawn from background knowledge and observations.

visual dictionary - visualizationWhen students use this comprehension strategy, you may hear them say…

  • I am getting a picture…
  • I can see (smell, hear, taste)…
  • I have a picture in my head…

Some tactics that teachers might use to promote visualization include:

Summarizing and Synthesizing

This comprehension strategy involves students recalling, retelling, creating new meaning, and remembering information. Synthesizing information allows us to see the bigger picture as we read or observe. Thoughtful readers merge their thinking with information to come to a more complete understanding. It is important that teachers teach learners to:

  • Add to their knowledge base.
  • Paraphrase information
  • Move from facts to ideas.

Summarizing and synthesizing are often used as synonyms. While they are related, they are different strategies that readers use. Sarah Eaton, a professor at the University of Calgary (2010, Summarizing vs Synthesizing), identifies these differences:

SummarizingSynthesizing
A basic reading technique.An advanced reading technique.
Pulls together information in order to highlight the important points.Pulls together information not only to highlight the important points, but also to draw your own conclusions.
Re-iterates the information.Combines and contrasts information from different sources.
Shows what the original authors wrote.Not only reflects your knowledge about what the original authors wrote, but also creates something new out of two or more pieces of writing.
Addresses one set of information (e.g. article, chapter, document) at a time. Each source remains distinct.Combines parts and elements from a variety of sources into one unified entity.
Presents a cursory overview.Focuses on both main ideas and details.
Demonstrates an understanding of the overall meaning.Achieves new insight.

Summarizing is taking the details of information apart while synthesizing is putting those details back together into a new and unique whole.

visual dictionary - summarizing and synthesizingWhen students use this comprehension strategy, you may hear them say…

  • I never knew… now I know…
  • I think the big idea is…
  • I have learned that…
  • Now I understand that…

Some tactics that teachers might use to promote summarizing and synthesizing include:

When do we explicitly use Comprehension Strategy Tactics?

If the information that we are having students interact with is complex, it is important to use instructional methods that help them make meaning. As well, if we notice that students are struggling with a specific skill or content area, we can view comprehension strategy instruction a possible solution to those learning barriers. Teaching with comprehension in mind will lead to increased cognitive engagement and deeper meaning-making.

Eaton, S. E. (2010, September 26). Reading Strategy: The difference between summarizing and synthesizing. Retrieved from http://www.drsaraheaton.wordpress.com

Johanson, T., & Broughton, D. (2014). Exploring Comprehension in Physics. Saskatoon: McDowell Foundation.

Keene, E., & Zimmermann, S. (1997). Mosaic of Thought: Teaching Comprehension in a Readers Workshop. Portsmouth: Heinemann.

Public Education & Business Coalition. (n.d.). Thinking Strategies for Learners: A guide to PEBC’s professional development in reading, writing, mathematics and information literacy. Retrieved December 15, 2018, from Public Education & Business Coalition: https://www.pebc.org/wp-content/uploads/publications/thinking-strategies.pdf

Saskatchewan Ministry of Education. (2008). English Language Arts 6. Retrieved from Saskatchewan Curriculum: https://www.curriculum.gov.sk.ca/bbcswebdav/library/curricula/English/English_Language_Arts/English_Language_Arts_6_2008.pdf

Strategic Planning: A Process of Empowerment

Rather than a deficit view of what your organization is not doing, or not doing well, a strategic planning process should identify where you want to go, what you are already doing that might help, and how you might leverage the strengths of your organization to get there. By empowering your employees with a positively intentional view of your organization’s impact, it is possible to design a future state and the steps to get there. When an organization works with others to achieve its goals, identifying the influence you have on others and the influence they have on you, along with the steps you might take to achieve the influence you are seeking should be a part of your strategic action plan.

There are three key theories of strategic planning that work well when viewed as part of a holistic process:

  1. Appreciative Inquiry
  2. Outcome Mapping
  3. Logic Modelling

Appreciative Inquiry

Appreciative Inquiry

There are a series of stages built into the Appreciative Inquiry process:

1. Discovery: What are we currently doing well?

  • Ideas are themed and patterns emerge related to organizational strengths. This process allows organizations to focus on positive capacity.

2. Dream: What is the world calling us to become?

  • What are the things about our organization that no matter how much we change, we want to continue into our new and different future?

3. Design: What should be our ideal state?

  • Co-constructed ideas are grounded in what we are currently doing well, opportunities that are apparent, and organizational capacity.

4. Destiny/Delivery:

  • How do we empower, learn and plan for actions to reach our ideal state?

 

Along with steps in the Appreciative Inquiry cycle, there are a number of foundational principles that guide conversations and planning:

Appreciative Inquiry Principles

Outcome Mapping

Where does outcome mapping fit into Appreciative Inquiry? Within the Design Phase, those organizations that work collaboratively with other groups in a mutually influential role can utilize facets of outcome mapping to identify actions, outcomes, and desirable observable behaviours.

Strategic action planning and program evaluation involve the following steps:

Strategic Planning Steps

In order to have an impact, people and organizations need to change behaviours. This occurs within the Outcomes stage. When we see ourselves and our organization as a part of a large web of interdependent entities in relationship with one another, we can view change as

  • Continuous
  • Complex
  • Non-linear
  • Multidirectional
  • Not controllable

People and organizations contribute to the goals of others through influence rather than control.

Program Evaluation as Formative Assessment

Program evaluation is built into strategic planning so that progress can be monitored. When viewed as formative assessment, program evaluation can provide real-time information to inform decisions regarding action plans, inputs, and innovations within your organization. Are the actions you are taking resulting in the outcomes you have identified?

Traditional Evaluations

Evaluation as Formative Assessment

Purpose Supports improvement, summative tests, and accountability. Renders definitive judgments of success or failure. Supports development of innovation and adaptation in dynamic environments. Provides feedback, generate learnings, support direction or affirm changes in direction.
Roles & Relationships Positioned as an outsider to assure independence and objectivity. Positioned as an internal team function and ongoing interpretive processes.
Accountability Focused on and directed to external authorities and funders. Centered on the innovators’ deep sense of fundamental values and commitments.
Design Design the evaluation based on linear cause-effect logic models. Design the evaluation to capture system dynamics, interdependencies, and emergent interconnections.
Measurement Measure performance and success against pre-determined goals and SMART outcomes. Develops measures and tracking mechanisms quickly as outcomes emerge and evolve.
Evaluation results Aim to produce generalizable findings across time and space.

Evaluation engenders fear of failure.

Aim to produce context-specific understandings that inform ongoing innovation.

Evaluation supports hunger for learning.

Complexity and uncertainty To control and locate blame for failures. Learning to respond to lack of control and stay in touch with what’s unfolding and thereby respond strategically.

(Quinn Patton, 2006)

Boundary PartnersBoundary Partners

Boundary partners are a term used within Outcome Mapping to describe those groups or organizations that you work with directly and anticipate opportunities to be mutually influential. Outcome Mapping identifies behavioural changes in your boundary partners as being a key measurable towards your goals. This is due to the fact that “development is done by and for people. Although a program can influence the achievement of outcomes, it cannot control them. This is because ultimately the responsibility rests with the people affected” (Earl, 2008).

Progress Markers

Progress markers (Earl, 2008) are a set of statements describing a progression of changed behaviours in a boundary partner. These describe:

  • Actions
  • Activities
  • Relationships

Leading to the ideal outcome. These markers show the complexity of the change process and have the following characteristics:

  • Can be monitored and observed
  • Permit on-going assessment of boundary partner progress, including unintended results

The ladder of change can be applied to any progress marker:

  1. Beginning: Expect to see.
  2. Mid-Term: Like to see.
  3. Final: Love to see.

Logic Model

A logic model (Taylor-Powell & Henert, 2008) has many different forms and is a structured way to note specific inputs and activities of an organization and how they lead to outcomes over short, medium and long-term timelines. A logic model can be used in conjunction with other strategic planning processes and is a useful organizer.

Logic Model

When using a Strategic Planning Logic Model, a process might be to:

  1. Identify your vision and future state.
    • If using Appreciative Inquiry, use your thinking about your future state here.
  2. Identify your goal areas needed to reach that future state.
    • This should include those initiatives that you are currently doing well, what needs to change and new innovations.
  3. Determine your outcomes as short, medium and long-term.
    • If using Outcome Mapping, use your thinking about Boundary Partner Progress Markers here.
  4. Generate your inputs, including time, resources, people.
    • Realistic resources may have an impact on timelines for outcomes.
  5. Determine your outputs and activities and who will participate in them.
    • These may be viewed as deliverables.
  6. Identify your measurable data.
    • What can be tracked? What does that data tell you?
    • What data do you currently have access to? What requires a collection method to be developed?
    • Refer back to your observables in outcomes and outputs. Have you captured these in your data? Will your data story give you a picture of this initiative?

By working through an integrated process for strategic planning, you can empower your organization to look beyond a deficit view of present state and work towards a desired future. By having an action plan for the steps to getting to your future state, it is possible to measure progress as formative assessment, providing a continuous feedback loop for your organization.

References

Earl, S. (2008, June 20). Outcome Mapping Pt 1. Retrieved December 13, 2018, from https://www.youtube.com/watch?v=fPL_KEUawnc

Quinn Patton, M. (2006). Evaluation for the Way We Work. The Non-Profit Quarterly(Spring), 28-33. Retrieved December 13, 2018, from https://www.scribd.com/document/8233067/Michael-Quinn-Patton-Developmental-Evaluation-2006#download

Stavros, J., Godwin, L., & Cooperrider, D. (2015). Appreciative Inquiry: Organization Development and the Strengths Revolution. In W. Rothwell, R. Sullivan, & J. Stavros, Practicing Organization Development: Leading Transformational Change (pp. 96-116). Wiley Blackwell.

Taylor-Powell, E., & Henert, E. (2008, February). Developing a Logic Model: Teaching and Training Guide. Retrieved December 13, 2018, from https://peerta.acf.hhs.gov/sites/default/files/public/uploaded_files/Logic%20Model%20Guide.pdf

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