Workshop Blog

Designing PD That Teachers Deserve

I have had the pleasure of working with two different organizations recently, helping their staff to understand some basic principles of designing professional learning experiences for teachers. Designing professional learning deserves as much care and attention as the planning that we expect classroom teachers to give to their classroom instruction. We do not accept undifferentiated teacher lecture as the only pedagogy in classrooms, so it is important that we design professional learning that is

  • NOT a prescriptive module that does not change, regardless of what learners need
  • NOT solely lecture-style presentation where we tell them information and leave the meaning making and application to teachers after an event.

In my decade of designing and facilitating professional learning and teaching others to design professional learning, I have been seeking out and creating ways to approach workshop design. My goal is to ensure that I provide rich, authentic, practical and differentiated adult learning to teachers and related professionals. I firmly believe that a day of teacher workshop must be as or more important than a day that teacher would have had with their students. And a day with their students is SO important.

In my learning journey, I have discovered a few key things that are the foundation for every workshop that I create and facilitate.

Expect to Learn from Participants: Partnership Principles

One of my first learning opportunities about designing professional learning was Jim Knight’s Partnership Principles. His philosophy is very simple – that the people who come to professional learning are equal in every way to the facilitators of that learning. There is no hierarchy in learning, we are colleagues and partners.

Jim Knight’s Partnership Principles identify that if we have a mindset of equality, where our learners have choice and voice with professional learning, we will create interactions that encourage dialogue, reflection where we both can learn. An ultimately, the goal is for praxis, or application and transfer of learning into teacher contexts and classrooms.

Vision Our Impact: What Change Are We Hoping For?

It is important to see what changes we are hoping for in teacher behavior, resulting in an impact on student learning. Following Thomas Guskey’s Five Levels of Evaluating Professional Development backwards, it is possible to pose questions that can be pre-thinking before we begin designing learning. This process helps us to identify WHY we are providing this professional learning. As Simon Sinek has identified in his talk on The Golden Circle, we often think about the WHAT and the HOW, but it is the WHY that inspires us. When we, as facilitators, know why, we can share that passion and enthusiasm with our adult learners. A helpful tool is to use a Thinking Map, along with the following questions:

Ask Teachers What They Need

Ideally, we can engage teacher learners before our learning event to find out what learners need. This might be informed by:

  • Observations of student behaviours – what changes are needed?
  • Observations of student learning – what gaps or areas do students need a greater focus on?
  • Observations of teacher knowledge – what would learners like to know more about or change in their own understanding?

If it is not possible to have this conversation before learning, there are different facilitation processes that can be done that can inform our facilitation. These include:

  1. Snowball – ask participants
    • What do you know about this topic?
    • What do you wonder about this topic?
  2. Notice and Wonder – provide some type of visual or media experience and then ask
    • What do you notice about this?
    • What do you wonder about this?
  3. Touch Each Page and then Professional Question Generation
    • The Touch Each Page strategy will create a focus for professional inquiry through the day.
    • Generating Questions:
      • Group Generating and Monitoring Questions – participants work in small groups to identify questions that they would like to answer.
      • Personal Inquiry – participants identify a question that they most want to answer through the day. This is put onto a sticky note that they revisit and discuss at the end of the day with a colleague.

Have an Assessment Plan: Guskey’s 5 Levels

Thomas Guskey has identified five levels of evaluation to consider when understanding the efficacy of any professional learning experience in his article “Does it Make a Difference? Evaluating Professional Development”. Too often, we take in data around student outcomes and teacher satisfaction but neglect to identify the levels in between that allow us as facilitators to draw conclusions and connections between the professional learning that we are engaging in and the impact on students.

As Guskey has stated, “Good evaluations don’t have to be complicated. They simply require thoughtful planning, the ability to ask good questions, and a basic understanding of how to find valid answers” (Guskey, 2002). It is important as we evaluate our professional learning experiences that we are looking for evidence around its efficacy, not proof that it is making a difference. Most often, there are many different professional experiences that are impacting student learning, and to identify the exact scope and impact of any one initiative is nearly impossible. Instead, it is useful to gather evidence, both qualitative and quantitative, that identifies shifts and possible contributors to changes in student learning.

Guskey’s Five Levels of Evaluating Professional Development allow us to consider the types of questions that we might ask participants during or after professional learning. Facilitators who can connect with teachers after professional learning can gather data regarding impact on student outcomes and participant use of knowledge and skills.

If you are only in contact with educators during a session, it is possible to assess levels one through three, and measure teacher intent to implement using an Agenda Assessment. An agenda assessment is an innovation that combines an agenda with an assessment of learning and can be completed throughout a professional learning experience. This information can give insight into the effectiveness of a workshop or other learning experience.

Plan for Flexibility: Have a Plan that Allows for Change

A useful planning structure is a Facilitation Guide. Like a lesson plan that a teacher might use in a classroom, a facilitation guide identifies content, process, assessment, timing and materials. This simple structure helps facilitators see how content is chunked during the day, and the sequence of instructional strategies.

Content: This is the sequence of main ideas that flows through the day. By chunking content, it is relatively easy for a facilitator to skip or skim over particular ideas. This might occur if

  1. Teachers have already identified that they know a specific piece of information; or
  2. Time does not allow for all of the concepts in the day to be covered.

Process: This column identifies the instructional strategies and key questions that facilitators might pose to encourage thinking.

Assessment: This column allows facilitators to predict what they think participants might do or say during a specific part of the workshop. It is helpful to identify

  1. what people might say if they have a misconception; or
  2. what we are looking for in participant responses that indicates that they understand.  

Timing: Just as it states, this column allows facilitators to predict the length of time that a specific process will take. This helps to know whether the workshop is at, ahead or behind timelines outlined.

Materials: This column has us list materials or resources that are used in that chunk of a workshop.

Incorporate Meaning Making Strategies: Differentiate Learning

It is important that we choose processes for learning that fit the content and amount of time provided. Considering Dylan Wiliam’s Formative Assessment Strategies, instructional strategies in professional learning are particularly powerful when they:

So, where do we find these strategies? There are many useful resources. Some of them include:

It may seem like there are many layers and lots of time needed to plan effective professional learning, but our teachers and ultimately student learning deserve our investment.

Differentiating Instruction – Why, How, What?

How often have we been in a conversation with a colleague about trying to meet the needs of all of our students, and we hear the dreaded phrase “well, just differentiate”… this blanket statement can bring about visions of creating 18 different lesson plans for our 18 students. This is not sustainable, so what is differentiation REALLY? How do we meet the needs of diverse learners and keep our sanity?

Picture Feedback 2

Workshops focussing on differentiation are, ironically, often not differentiated. It is important that all professional learning, including those experiences based on the topic of differentiation, attempt to have teachers experience differentiated learning as well as reinforce the foundations of how and why we differentiate content, process, product and environment for students. 

Planning for Differentiation

It is important to understand not only specific strategies but to also know why we might differentiate. What information do we need as teachers in order to plan appropriately for our individual students as well as our whole class experiences? We need to know a combination of Learning Styles, Multiple Intelligences, content readiness, and student interests in order to Plan for Differentiation.

Planning Differentiation

This information can be compiled into a Learner Profile Card or a Whole-Class Preferences Summary Chart to allow both students and teachers to know what and how learners might learn best.

Something that is often an ‘aha’ for adults is to consider whether they are “Think to Talk or Talk to Think” learners. If someone is a think-to-talker and is forced to jump into group work without first having the chance to get their thoughts in order, they may have a feeling of being unsafe expressing their ideas. If a talk-to-thinker is forced to read quietly before they are allowed to talk, they may find that their minds wander and are unable to focus. This same sense of safety is true for student learners as well.

One of the foundational researchers in the area of differentiation is Carol Tomlinson, who describes differentiation as

  1. Being curious about our students,
  2. Having relationships between teachers and students; and
  3. Providing a variety of learning experiences to learners

Differentiating Content

Why:

Differentiating content allows you to address gaps in understanding to build readiness. We know in literacy that activating prior knowledge is essential for students to make connections to new learning. This is true in other subjects as well. Assessing prior knowledge allows gaps to be addressed before new concepts are introduced. Differentiating content allows students to ACCESS information and learning.

What:

Your curriculum drives the knowledge, concepts, skills, and understandings a student needs to know and use. While the curricular outcome cannot change for individual students, the delivery format for content such as video, readings, audio, reading level can be differentiated. Content can also be chunked, shared through visual graphic organizers, or addressed through jigsaws to reduce the volume of information each individual needs to interact with. Themes can be based on personal interest to increase interest and understanding if a specific topic is not required by the curriculum.

How:

  • Use pre-assessment to determine where students need to begin, then match students with appropriate activities. Pre-assessments may include:
    Pciture Feedback 4
    • Student/teacher discussion,
    • Begin a KWL chart – what we know/want to know/learned,
    • Journal – what you already know about,
    • Brain dump – list all of the things you know about a topic, cluster with other class members, and
    • Snowball.
  • Use texts or novels at more than one reading level.
  • Present information through both whole-to-part and part-to-whole.
  • Use a variety of reading-buddy arrangements to support and challenge students when working with different texts.
  • Re-teach students pre-skills or provide enrichment for students who already demonstrate an understanding of pre-skills.
  • Use texts, video or different media to convey information.
  • Use Bloom’s taxonomy or Webb’s depth of knowledge to encourage thinking about content at several levels.

Differentiation Process

Why:

Differentiating process is about how students make sense of new learning. What is happening in each individual brain is based on their learning preferences, multiple intelligences, and background. Learners need time to take in, reflect on and make sense of new learning before moving on. Processes help students monitor their comprehension and determine what they do and do not understand. Learning processes also allow teachers to formatively assess student progress and provide feedback in real time.

What:

There are many different words used to describe learning processes – instructional strategies, discursive strategies, comprehension strategies… all of these are ways that learners interact with and make sense of new learning. Providing more or less structured support for learning, planning for a variety of instructional strategies based on the variety of learning styles in a classroom during a unit of study, and providing opportunities for self-reflection and self-assessment, and providing individual, pair/small group and whole group learning experiences are some key ideas for differentiation process.

How:

  • Assess learning styles, multiple intelligences, learning preferences, etc. to understand individual learning profiles as well as your class profile.
  • Use tiered activities that allow all students to work on the same outcome but with different levels of support.
  • Provide different learning experiences based on interests – i.e. when exploring mixtures and solutions, some students might choose to learn concepts through cooking, while others may learn concepts through art.
  • When planning a unit of study, ensure that concepts are interacted with using a variety of modes. For example, in mathematics, a planning form for math could be based on the idea of multiple representations of mathematical ideas:
Math Example Differentiation
  • Use a variety of comprehension strategy tactics.
  • Provide choice for students for how they are going to take notes, summarize information, make connections.
  • Use reflective strategies, such as:
  • Literature Circles(which also support content and product differentiation).
  • Different classroom structures, such as stations/centers, choice boards, flexible grouping all allow for different processes to be occurring simultaneously.

Differentiating Product

Why:

Differentiating product allows for student choice and allows learners to use their strengths to represent their understanding. Product choices all align to curricular outcomes, so learning is not compromised. Student voice and choice increase learner engagement. Products are the way that students represent their thinking about a curricular outcome. Differentiating the type of product being created allows you to see what they know about the curricular topic rather than the skill they needed to package that representation.

What:

Product differentiation is often cited as the most common form of differentiation and is often in the form of choices. You as the teacher may provide those choices and students pick from a variety of formats, you may have students propose their own designs or a combination of the two. How much responsibility and autonomy you provide for your students will depend on factors such as student understanding of their own strengths, age and time. When providing choice, it is important to co-construct clear criteria for success so that all products, regardless of form, are all being assessed on curricular outcomes rather than the form of a product. A rule of thumb is that the same checklist/rubric/assessment tool should be able to be used for all products on the same outcome, whether they are a paper, video, play, board game, etc.

How:

  • Allow students to help design product choices.
  • Co-construct assessment criteria.
  • Allow for varied working arrangements – individual, pair, group
  • Provide for or encourage students accessing a variety of resources.
  • Ensure that all products are at the same level of Bloom’s Taxonomy or Webb’s Depth of Knowledge.
  • Use a common assessment tool (checklist, rubric, etc.).

Conclusion:

When teachers plan by connecting content, process, product and learning product with student readiness, interests and learning profiles, students are more engaged and are able to understand ideas with a higher level of complexity.

Works Cited

McCarthy, J. (2015, August 28). 3 Ways to Plan for Diverse Learners. Retrieved from Edutopia: https://www.edutopia.org/blog/differentiated-instruction-ways-to-plan-john-mccarthy

New South Wales Education. (2015). Decide What to Differentiate. Retrieved from Phase 4 – Differentiating Learning: http://www.ssgt.nsw.edu.au/differentiating_learning.htm

Teaching Number Operations

Addition, subtraction, multiplication and division are foundational skills that are applied to many mathematical concepts. Often, when we are hoping for student automaticity and fluency in numbers, number operations are what we are talking about.

Mathematical Models

Models are the way we are representing numbers so that we can do number operations. There are a number of different models that are helpful to students understanding number operations.

Models that Emphasize 10

Models that Emphasize Place Value

Models that Emphasize Patterns

Models that Emphasize Partitioning Number

The Importance of Partitioning Numbers

Regardless of what number operation we are talking about, it is important that children are able to break numbers into parts.

Friendly Numbers – children are often able to understand number operations with ‘friendly’ numbers like 2, 5, and 10. Breaking a 7 into a  and a 2 allows us to use number facts that are more familiar.

Place Value Partitioning – when we are working with multi-digit numbers, it is helpful for us to break numbers up into the values of their digits – for example, 327 is 300 + 20 + 7.

Number Operation Strategies

There are many different strategies that children use to perform number operations. A misconception is that all children need to know and use all strategies. It is important for us to expose children to different strategies through classroom discussion and routines such as number talks and number strings. When combined with Margaret Smith’s ideas around Orchestrating Classroom Discussion, we can set a task for students and

  1. Predict what strategies they might use. Order these from least to most complex.
  2. Observe students doing mathematical tasks – using white boards allows us to see their thinking. We can then identify different strategies being used.
  3. Have students share their thinking in an order from least to most complex. This should not include every child sharing for every task. A small handful of children sharing in a logical order can help students understand the next more complex solution. In this way, children are being exposed to other strategies, will be able to understand those that are close to their own, and increase the sophistication of their thinking.
Strategies Connection to Addition Connection to Multiplication
Counting: This is a common strategy when one of the numbers is small. Addition by counting or counting on from one number. Ex: 25 + 7 = 25, 26, 27, 28, 29, 30, 31, 32.   Skip counting by one of the numbers being multiplied. 9 x 5 = 9, 18, 27, 36, 45  
Decomposing Numbers: breaking numbers apart. Adding friendly numbers. Ex: when you need to add 12, breaking it into +10 and then +2 more.  

Making 10. Ex: when adding 5 + 7, recognizing that 5 + 5 = 10, and so it is 10 + 2 more = 12.  

Breaking one or both numbers into place value. Ex: 23 + 47 is 20 + 40; 3 + 7
Multiplying friendly numbers. Ex: when you need to multiply by 6, break it into x 5 and 1 more.          




Partial Products: Breaking one or both numbers into place value. Ex: 23 x 47 is (20 + 3) x (40 + 7)
Compensation: this is very common when a number is close to 10. Rounding one of the numbers to a friendly number, then compensating the answer at the end for the difference. Ex: 36 + 9 is close to 36 + 10, subtract 1. Ex: 36 + 11 is close to 36 + 10, add 1. Rounding one of the numbers to a friendly number, then compensating the answer at the end for the difference. Ex: 99 x 5 is close to 100 x 5, subtract 5 Ex: 101 x 5 is close to 100 x , add 5
Double/Half Recognizing that 4 + 4 is double 4, or 8. Recognizing that 4 + 3 is almost double 4, subtract 1. Recognizing that 5 x a number is the same as ½ of 10 x a number. Ex: 9 x 5 is half of 9 x 10 = 45
Standard Algorithm Traditional algorithm, symbolic regrouping. Traditional algorithm, symbolic regrouping.

A Bridge between Addition and Multiplication: Doubles

  • Doubles are one way to think about adding a number to itself, as well as the start to multiplicative thinking.
  • Doubles are an important bridge between adding and multiplication.
  • You can read more about teaching doubles here.

Addition and Subtraction

Addition is the bringing together of two or more numbers, or quantities to make a new total.

Sometimes, when we add numbers, the total in a given place value is more than 10. This means that we need to regroup, or carry, a digit to the next place. There is a great explanation of regrouping for addition and subtraction on Study.com.

Subtraction is the opposite operation to addition. For each set of three numbers, there are two subtraction and one addition number facts. These are called fact families. For example:

For the numbers 7, 3, 10:

                7 + 3 = 10

                10 – 3 = 7

                10 – 7 = 3

Fact families can be practiced using Number bonds or Missing Part cards.

As we move from single digit to multi-digit addition and subtraction, it is important that we maintain place value, and continue to move through the concrete to abstract continuum.

A helpful progression for teaching addition and subtraction can be found on the Math Smarts site.

Multiplication and Division

Conceptual Structures for Multiplication

Repeated Addition

  • This is the first structure that we introduce children to.
  • It builds on the understanding of addition but in the context of equal sized groups.

Rectangular Array/Area Model

  • This is often the second representation of multiplication introduced It is useful to show the commutative property that 3 x 4 = 4 x 3 = 12

Number Line

  • A number line can represent skip counting visually.

Scaling

  • Scaling is the most abstract structure, as it cannot be understood through counting.
  • Scaling is frequently used in everyday life when comparing quantities or measuring.

Single Digit Multiplication Facts

Multiplication facts should be introduced and mastered by relating to existing knowledge. If students are stuck in a ‘counting’ stage – either by ones or skip-counting to know their single-digit multiplication facts, it is important that they understand strategies beyond counting before they practice. Counting is a dangerous stage for students, as they can get stuck in this inefficient and often inaccurate stage. Students should not move to multi-digit multiplication before they understand multiplication strategies for single-digit multiplication.

  • It is important that students understand the commutative property 2 x 4 = 8 and 4 x 2 = 8.
  • 2 x 4 should be related to the addition fact 4 + 4 = 8, or double 4.
  • Using a multiplication table as a visual structure is helpful to see patterns in multiplication facts.

Mental Strategies Continuum

  • Same as (1 facts)
  • Doubles. (2 facts)
  • Doubles and 1 more (3 facts)
  • Double Doubles (4 facts)
  • Tens and fives (10, 5 facts)
  • Relating to tens (9 facts)
  • Remaining facts (6, 7, 8 facts)

Conceptual Structures for Division

Equal Grouping

In an equal grouping (quotition) question, the total number are known, and the size of each group is known.

  • The unknown is how many groups there are.

Equal Sharing

In an equal sharing (partition) question, the total number are known, and the number of groups is known.

  • The unknown is how many are in each group.

Number Line

Ratio

This is a comparison of the scale of two quantities and is often referred to as scale factor. This is a difficult concept as you can’t subtract to find the ratio.

Division Facts

Relate division facts back to multiplication facts families:

Ex)          6 x 8 = 48

                                8 x 6 = 48

                                48 ÷ 6 = 8

                                48 ÷ 8 = 6

Once students have understanding and fluency with single digit multiplication and division fact families they are ready to move on to multi-digit fact families.

So What do Students DO with Number Operations?

Simple computation is not enough for children to experience. They need to have opportunities to explore and wonder about numbers and how they work together. Regardless of the routine or task, children should be encouraged to use different concrete and pictorial models to show their thinking.

Some examples of rich interactions include:

Number Talks

  • Number talks promote classroom discussion. Combining number talks with visual or concrete models can help us see what students are thinking.

Number Strings

  • Number strings can help children see the pattern in number operations. They are helpful for children to see the pattern in number operations, which is the foundation for algebraic thinking.
  • You can see the structure for building number strings here.

SPLAT

  • SPLAT encourages both additive thinking and subitizing. More complex SPLAT lessons are also great for encouraging algebraic thinking with unknowns.

Problem Stories

  • Building problem stories are powerful for children to understand contexts of mathematics in their every day life.
  • Using real objects or pictures encourages children to see math in their environments.

Invitations

Games and Puzzles

  • There are so many games and puzzles that can have children play with number operations.

Open Middle Problems

  • Open middle problems allow for flexible thinking and exploration. You can see a sample here.

Building Coherent Teams

Michael Fullan (2016) states that coherence is “a shared depth of understanding about the purpose and nature of the work in the minds and actions individually and especially collectively” and is not about specific strategies, frameworks or alignment. So, how might we build coherent teams? How do we determine the ‘right’ actions and de-emphasize actions that are distractions? How might we focus on actions that enhance our collective as well as our autonomy? There are some processes and skills that are helpful.

Positive Communication

To build coherent teams, we need to know and practice communication skills, including paraphrasing and posing questions. A general conversation flow includes:

The Art of Paraphrase

“The purposeful use of paraphrase signals our full attention. It communicates that we understand the teacher’s thoughts, concerns, questions and ideas; or that we are trying to … well-crafted paraphrases align the speaker and responder, establishing understanding and communicating regard. Questions, no matter how well-intentioned, distance by degrees, the asker from the asked.”

(Adapted from Wellman and Lipton)

Things to keep in mind when paraphrasing:

  • Attend fully.
  • Listen with the intention to understand.
  • Capture the essence of the message but in a shorter format.
  • Reflect the essence of voice, tone and gesture.
  • Paraphrase before asking a question.
  • Use the pronoun “you” instead of “I.”

Intentions of Paraphrasing

Well-crafted paraphrases with appropriate pauses trigger more thoughtful responses than questions can alone. Three types of paraphrase, shown in the chart below, widen the range of possible responses. Each type supports relationship and thinking but the paraphrase that shifts the level of abstraction is more likely to create new levels of understanding. Conversations that utilize paraphrasing often move through a pattern of acknowledging to summarizing to abstracting, but there is no right pathway for the conversations.

Types of Questions

Horn and Metler-Armijo (Toolkit for Mentor Practice, 2010) identify three types of questions that are useful for professional conversations:

  • Clarifying questions – are asked to further understanding of the questioner. These types of questions convey that the questioner is actively interested.
  • Probing questions – are asked to have the speaker think more deeply about the concerns, challenges, or actions being taken. These types of questions dig into ideas to move from generalizations to specific ideas.
  • Mediational questions – are “intentionally designed to engage and transform the other person’s thinking and perspective” (Costa and Garmston, 2002). These types of questions are designed to open up and broaden thinking.

Mediational Questions

A special comment on “Why”…

Why questions are part of our everyday language. Why are you late? Why do you not have a pencil? Why are you doing that?

When we are having a conversation that may be emotional or highly charged, a question that begins with “Why” may create a sense of defensiveness. Consider a situation where someone has made a certain decision. Compare the reaction to “Why have you done this action?” vs “What is the impact your decision has had on…?”. A question that begins “What” or “How” is often more thought provoking and has less potential to create a defensive response.

Rectangle: Rounded Corners: Communication skills are key to building coherent teams, as they allow deep conversations to occur amongst team members, provoking thought through active listening.

Liberating Structures

Liberating structures, when used regularly, allow all team members the opportunity to work together to produce solutions, ideas and feel that everyone is contributing to an organization’s next steps. It is possible for every person to generate ideas and lead change.

Integrated~Autonomy

When considering how to best meet the needs of a system and the schools within a system, it is important that we view centralization/standardization and autonomy as both achievable and desirable rather than viewing them as opposite and competing interests. The Integrated~Autonomy liberating structure can help us to:

  • Develop innovative strategies to move forward.
  • Avoid wild swings in policies, programs or structures.
  • Evaluate decisions by asking “are we boosting both Coherence and Autonomy?”.
  • Increase quality of communication between school-based and Increase quality of communication between school-based and central office leaders.

Imagine actions that work towards BOTH increased standardization/centralization and increased Autonomy.

Some Examples

  • Attendance policies and consequences for non-attendance – what policies should be set centrally and which decisions should be made locally?
  • Planning documents required for hand-in/approval – format, timing and requirements for year, unit and lesson plans?
  • Parent conferences and reporting communication – what determined (format, process, content) centrally and what locally?

Structuring the Invitation:

  • Explore the question: Will our purpose be best served by increased local autonomy, including customization and site-based decision-making OR will our purpose be best served by increased coherence, including integration, standardization and centralized decision-making?
  • How might we be more coherent AND more autonomous at the same time?

Troika

This collaborative problem-solving strategy allows for colleagues to share possible solutions in a safe, non-judgmental environment.

In groups of three, learners sit in a triangle facing one another with no table between them. One person is the ‘client’, and the other two are the ‘consultants’.

  1. The client describes their dilemma, barrier or issue for about 2 minutes. The consultants might ask clarifying questions at this time.
  2. The client turns their chair so that their back is to the two consultants. The consultants discuss possible solutions to the client’s issue without any input, affirmation or cues from the client. The client might write down those suggestions that are most helpful. This might last for 2 – 4 minutes.
  3. The client turns around and summarizes what suggestions are most helpful that they might try.

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

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