What were many of us MOST looking forward to for Christmas? Food, Fun and Family… Fun in our family over the years has been board games, cards and dice games. And then new health orders came to Saskatchewan and that hope seemed to be dashed… BUT… there was a huge ‘aha’ when I was asked to design and facilitate a “Let’s Play: Math Games Online workshop” this past week. I put my research hat on and found some online platforms for play. There are SO many cool fun platforms that are FREE to everyone. There will be Cribbage for Christmas after all!!
I have always believed that my confidence and competence in math came from the games I played as a child. Cribbage with my Grandpa and Great Grandpa, Monopoly with my friend Tommy, Go Fish with my sister, 31 with my Mom and Dad… So, how might we play these games online with Jori and Michael in Martensville, Erin in Comox, and Adam in Saskatoon? And better yet, how do we play them with the kids’ cousins Paige in Halifax, Amanda and Christian in Winnipeg, and then there is Auntie Sandra in Melfort and Grandma Carol down in Mesa this Christmas? My family is FAR too large to list everyone here, but you get the idea. Here are some games and platforms that might bring some cheer to your homes and families over the holidays.
Each of the following does NOT require an account or sign in. For each, you:
Start a game.
Copy the link and send it out by text or email to your game friends.
Set up a phone call or video call so that you can talk to everyone in the game. (Did you know that your iPhone can create a group call up to 5 people??) Or use Zoom, Google Meet, Facebook Rooms, What’s App… SO many possibilities. If two of you are in the same house on your own devices, consider either using your phone on speaker, or each of you use headphones/ear buds so you don’t get sound feedback.
Each of these is designed for each player to have their own device – they seem to work on computers or tablet/iPad or smart phone.
We have rich Saskatchewan curricula, and an important step in planning is to make sense of what curriculum is asking students to know, do, and understand, and to connect to our local context. I just recently had a chance to work with the CTEP students in Cumberland House under the guidance of their instructor Lily McKay-Carrier. She calls this Nistota Curriculum (Understand Curriculum). Place matters, our students matter, and our own professional and personal knowledge matters when planning for instruction and assessment. Our professional judgment and expertise are what helps us design units of study that honour who are where we are teaching.
We know that outcomes are what students need to know, do and understand. They are the destination of instruction, while indicators are the ways that students might show us that they know.
So what is a process that we might use to make sense of curriculum? Mind mapping is a visual way to see connections between curricular ideas and link to our teaching context.
Steps for Mind Mapping:
Determine what course(s) and outcome(s) you are going to cluster into one unit of study.
If you are creating a cross-curricular unit, then you might want to start with one course and then link to others.
Some curricula cluster outcomes into strands that make sense to teach as one unit (i.e. science and social studies), while others make sense to cluster outcomes from different strands or teach them alone (i.e. mathematics), as a strand is too large.
Identify what concepts students would have interacted with BEFORE this unit that would have provided a foundation, and what concepts this unit feeds into next.
Read over the outcomes to get a general sense of what the unit of study will be about. If you were to describe this unit to someone who is not a teacher, what might you say in a sentence or two?
Highlight the main concepts identified in the outcomes and indicators. These are often the NOUNS.
Mind map the main concepts to see how they connect. Often, there is repetition between outcomes, so this helps to streamline the unit.
Ask yourself what activities based on your community or your personal and professional knowledge might connect to curricular ideas. Add these to your mind map.
Sample Unit: Mind Map of Diversity of Living Things generated in collaboration with CTEP students fall, 2020.
Once you have generated teaching ideas, ask yourself if these honour the intent of the indicators in your curriculum. If a student did these things, would they be able to show that they know, do or understand this outcome?
Developing your Mind Map into a Unit of Study
Once you have created a mind map of key concepts and teaching activities, you can
develop essential questions that pull together the unit.
Develop an instructional sequence that includes:
Learning Activities
Assessment – both formative and summative
Materials/resources required
You can see the beginning of a draft unit of study created in collaboration with CTEP students in fall, 2020 focusing on Diversity of Life in Science 6.
I had the chance to work with the wonderful staff at Rossignol Elementary in Ile-a-la-Crosse this winter. They, like many of us, have been wondering how to support their students to be more engaged writers. They wondered:
How do we engage student writers? How do we make our students feel that they ARE writers and authors in our classrooms? There are so many blogs and ideas written on this topic, but what might work for OUR students?
There are many blogs and resources that are useful when seeking out new and innovative ideas to try. Some good ones include (but are certainly not limited to!):
Each of these articles is full of lists of creative strategies. But what works for YOUR students? This is where professional conversations and thinking about what students you have in your context can help.
We often ponder the question “Why don’t our students write more?”… something to consider is how much writing we do ourselves as adults. I have to admit that prior to creating this workshop blog, I might have gone weeks without writing outside of emails or filling in forms. To give insight into some of the barriers that our students face when writing, it is important for us to consider our own writing habits (and maybe fears!). How do we encourage ourselves as writers? My epiphany when planning for this workshop was that perhaps writing professional development needs to following the same framework that we might use for our students.
Adrienne Gear (2014) suggests the following lesson framework for each nonfiction form:
An introduction to the features of the nonfiction form.
This can be done by analyzing published examples of a nonfiction form.
Independent write and Whole-class write can be woven together in a We DO – You DO cycle.
With this framework in mind, the teachers of Rossignol Elementary worked in collaborative groups to write the following ideas for engaging their student writers:
Shared Writing About Writing
Engaging Student Writers is about the things that we can do as teachers to encourage students to write across all curricula. There are many different strategies that fit different grade levels and different content areas. It is important that we use our professional judgement to combine our existing professional knowledge, our knowledge of our students, and the new information we learn from our colleagues and research.
Drawing and Talking to Encourage Writing in Young Children
To encourage young children to write, have them group together to talk about a common experience (sliding, wiener roast, building a snowman). As children share information, the teacher can capture the vocabulary they are using.
Teachers can
Record on a chart or individual cards/word strips
Include a picture
Display in the classroom
Children can
take those word strips/cards and draw their own picture
describe/talk about their picture with an adult or older student
label the picture (either by the child or the adult/older student)
Differentiating Writing
How might we differentiate next steps? The sequence will depend on the age and ability of young writers.
Younger writers might have an older student or adult scribe a sentence for them. They can leave enough space underneath for the child to copy the words below.
Older writers might use the labels on their picture to write a sentence or sentences about their picture.
If students’ oral language skills are low, they can communicate meaning through the use of point pictures or flash cards. Key ideas related to the pictures can be created in advance by the teacher.
Extra Time for Encouraging Elementary Writers
There are many ways that we can encourage our elementary-aged writers in our classrooms.
When we give more time to write, we encourage writers to write more often. Allowing more time to organize their thoughts and ideas, using graphic organizers, modelling writing and brainstorming together can all contribute to student confidence.
Deadlines and expectations need to be communicated clearly so that students understand what needs to be produced and when it needs to be produced by.
Use technology like voice typing for those who can’t write as fast as they think can reduce frustration and get ideas out.
For those students who may be shy, strategies like passing notes, chatting 1:1 with peers about the topic, and think-pair-share can help to build confidence.
With extra time and strategies to maximize the time, students are allowed to process their thoughts and make meaning. This can help to show them that they ARE good writers.
Comic Book Writing for Engaging Writers
Comic book writing is when students write the dialogue into a blank comic template. There are various templates that you can download from sites such as this one from Scholastic.
Where to start? You might start with a “We Do” comic strip, then move to “You Do” by having students write dialogue into a given template with pictures already provided. They can then move to creating independently by choosing their template, and eventually creating their own pictures, characters and words either by using clipart or drawing their own original comic.
Mentor texts can include Manga, Amulet, Archie Comics or Marvel Comics. The use of mentor texts is key to introduce and discuss examples of dialogue and how words and pictures interact.
Comic book writing can encourage all types of writers, as it is a unique combination of visual/writing skills to tell a story.
What We Learned About Teaching Writing
I am thankful to the teachers of Rossignol Elementary for agreeing to their writing going out to an authentic audience on my Workshop Blog. By experiencing shared writing as adult learners, we discovered what some of the underlying anxieties and fears might be for our students. Worry about being wrong, worry about not being good enough, experiencing how daunting a blank piece of paper is all contribute to deepening our understanding of what to do for our students.
As adults, we experienced the power of writing to deepen our understanding of writing to a much deeper level than just reading about writing might have done. New knowledge, combined with our professional knowledge and knowledge of our students can help us to encourage our students to BE writing, not just engage in writing.
Gear, A. (2014). Nonfiction Writing Power. Markham: Pembroke Publishers.
Johanson, T., & Broughton, D. (2014). Exploring Comprehension in Physics. Saskatoon: McDowell Foundation.
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?
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.
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
Being curious about our students,
Having relationships between teachers and students; and
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:
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:
Use a variety of comprehension strategy tactics.
Provide choice for students for how they are going to take notes, summarize information, make connections.
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.
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.
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.
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
Predict what strategies they might use. Order
these from least to most complex.
Observe students doing mathematical tasks –
using white boards allows us to see their thinking. We can then identify
different strategies being used.
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.
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:
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.
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.
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.
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.
Terry Johanson Consulting 