7 Moves for Effective Destreaming in Mathematics Classes

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Written by Jason To, Mathematics and Academic Pathways Coordinator for the TDSB

Since September 2021, math teachers across Ontario have been adjusting to a new classroom reality. No longer would students be streamed according to perceived ability or prior achievement into Academic and Applied classes. The practice was ended as it was shown to disproportionately lower academic outcomes for Black and Indigenous students, students from lower income backgrounds, and students with disabilities. To address this inequity, teachers are now tasked with meeting students’ needs in an inclusive, destreamed setting. While many teachers have successfully evolved their practice to meet this challenge, others are struggling to support all students while maintaining high academic standards.

To learn more about the inequities of destreaming, click here to read the report "Understanding de-streaming", created by ONTed.

A challenge I regularly hear from teachers across the province is meeting the needs of students with learning disabilities (LDs) in a destreamed math class. As a district leader in mathematics and destreaming for 10 years, I know this challenge very well. While every student with an LD is different and can present various math learning needs, what is in common is that their achievement in math is far below what they are capable of.

Click here to learn more about how learning disabilities can affect math learning.

In this article, I will briefly share 7 moves that teachers can take so that all students in a destreamed math classroom — but particularly those with learning disabilities — feel affirmed, build confidence, and learn high-level mathematics. While the focus will be on Grade 9 mathematics, many of the ideas in this article can be readily applied to earlier or later grades and in other subjects.

Move #1: Be a formative assessment fanatic

Formative assessment is one of the most powerful tools that a teacher has to meet students’ needs, particularly for students with LDs. After all, how do I teach effectively without knowing what students bring to the table and how they are progressing?

Examples of quick and easy formative assessments include:

• Polling: students can write on mini-whiteboards to answer multiple-choice or short answer questions and put up their responses for the teacher to see at a glance.
• Observations and conversations: As students work on math problems, walk around the classroom and observe how students are performing. Ask probing questions and have students elaborate on their written work to get a better sense of what they are thinking.
• Exit tickets: give one question to each student at the end of the lesson that hits your learning objective and collect their responses.

The key to formative assessment is what teachers do with the data that they have collected. Teachers should provide students with actionable feedback for improvement and immediate opportunities to try again. You may use the data to plan small-group interventions (more on that later). If most students demonstrate that they do not yet understand what was taught, then the teacher needs to reteach.

Move #2: Leverage curriculum expectations to review foundational skills

The design of the 2021 Grade 9 destreamed math course anticipates that some students enter Grade 9 with incomplete understanding of foundational math skills. That is why specific expectations related to integers and fractions were included in the curriculum revamp.

One such expectation is “apply an understanding of unit fractions and their relationship to other fractional amounts.” Why unit fractions? Because counting by unit fractions (e.g. “one-third, two-thirds, three-thirds, four-thirds,” etc.) is foundational in building fractions fluency. It is also important when decomposing unit fractions into smaller unit fractions and understanding equivalent fractions. For some students with LDs that do not have a strong foundational understanding of fractions, solidifying the use of unit fractions can go a long way.

Visit the Fractions Learning Pathways website to learn more about strengthening fractions fluency through unit fractions.

Move #3: Strategically use explicit instruction to reduce cognitive load

Explicit instruction is highlighted by the Ontario Ministry of Education as a high-impact instructional practice in mathematics that teachers should take advantage of.

To be clear, explicit instruction is not a 75-minute lecture. Rather, it is student-centred and teacher-led instruction that is intentionally designed to reduce cognitive load on students, since all learners have limited working memory to process new ideas.

Effective explicit instruction involves:

• Reviewing relevant prior learning that will be built upon
• Scaffolding and chunking new learning into manageable bits
• Going through worked examples and modelling steps while thinking aloud
• Using clear and precise language
• Providing active, guided practice to students after each chunk of learning
• Having students explain their learning to the teacher or to their peers (e.g. through a think-pair-share)
• Frequent formative assessment to check for student understanding and provide timely feedback

There is ample research evidence to indicate that students with LDs and other learning difficulties in math benefit from explicit instruction. However, the National Mathematics Advisory Panel in 2008 stated that there is no evidence to support its exclusive use for students with learning disabilities.

So the question is: when should explicit instruction be used in destreamed math classes to support all students, including those with LDs? I would suggest it for skills that would be overly time-consuming for most students to figure out through an inquiry approach due to a deficit in prior knowledge or fluency. Those skills will be different depending on the specific group of students.

A useful model to have when considering whether explicit instruction would be beneficial is the instructional hierarchy. It describes four stages of learning a skill: acquisition, fluency, generalization, and adaptation, with considerations for instruction at each stage. If trying to discover a math concept or skill will almost surely overload students’ working memory, then modelling through explicit instruction may be the most effective move.

Click here to view the handout "Instructional Hierarchy", created by the Center on Multi-Tiered Systems of Support.

Move #4: Provide guided inquiry-based instructional opportunities when appropriate

Inquiry-based approaches where students are figuring out new skills and strategies alongside teacher guidance are often most effective when students are at the generalization and adaptation stages of the instructional hierarchy. So, if a math concept can be developed by leveraging skills that almost all students are fluent in, then an inquiry-based approach can be very beneficial.

To illustrate this, I will use one of my favourite examples that I developed with my colleague Michelle Cavarretta on developing skills for simplifying algebraic expressions. The table below would be cut into strips of paper and groups of students would work together to simplify three expressions at a time. Expressions begin with moose and sheep, and then slowly transition into the variables of x and y. The key prior knowledge that this task depends on is students’ intuitive ability to sort things that are alike or different, which I would argue that almost all teenagers can easily do. By the end of the sequence, all students have not only learned how to group and simplify like terms, but they have had guided practice and immediate feedback throughout the learning process.

Example: Simplifying Algebraic Expressions

A popular research-informed framework for guided inquiry in mathematics is Building Thinking Classrooms, developed by Dr. Peter Liljedahl. One of the hallmarks of this approach is having students work collaboratively in triads on whiteboards. When groups work effectively, this approach reduces cognitive load by distributing it across group members. Group work, therefore, can be very helpful for some students with LDs with reduced working memory capacity.

Learning through inquiry is also a highly enjoyable process that can build student agency, which is often lacking in students with LDs due to their chronic struggles with learning math. The key to successful inquiry, however, is ensuring that students are set up for success throughout the experience.

Click here to visit the website "Building Thinking Classrooms" based on the work of Peter Liljedahl.

Move #5: Regularly use visual representations to support conceptual understanding

Visual representations not only help to make abstract concepts seem more tangible, but they can also assist with deepening understanding and retention. The dual-coding theory suggests that the pairing of words with images enhances each other during the learning process and supports stronger recall later in time.

Some powerful math visuals to leverage dual coding include:

• Number lines to illustrate operations with integers, comparing fractions, or the density of number sets,
• Online graphing tools, such as Desmos, to illustrate how the graph of a line changes when the equation of a line changes, or provide a supporting visual for slope calculations between two points,
• Balance scales on Polypad to complement an explanation of solving linear equations using the balanced method.

Not only can dual-coding support better retention of learning for students with LDs, but they can also enhance meaning-making and show that math concepts are interconnected ideas rather than a disjointed set of rules that must be memorized individually. In addition, as mathematics becomes increasingly abstract in secondary school, the need to link visuals with abstract representations becomes even greater for students with math learning difficulties.

Click here to learn more about Dual Coding and Learning Styles. 

Move #6: Engage students in deliberate retrieval tasks

Gaining fluency in mathematics involves being able to retrieve previously-learned ideas from long-term memory. Not surprisingly, regular retrieval of specific information strengthens the ability to do so in the future. Cognitive psychologists refer to this phenomenon as the testing effect (Roediger III & Butler, 2011).

Often, students with memory difficulties are provided with an accommodation on their individual education plan (IEP) for the use of memory aids (i.e. a “cheat sheet”) during math assessments. While a memory aid may be needed for a small segment of students with severe memory challenges, its use may actually hinder long-term memory retrieval for others by eliminating the need for students to recall facts and ideas that are provided on the memory aid.

Some examples of effective retrieval tasks that can be used regularly to strengthen fact retrieval include:

• No-stakes quizzes: give quizzes related to material that was just learned, as well as concepts learned previously. These quizzes should not count for grades, and feedback can be provided to students for improvement.
• Interleave questions: when assigning questions for students to try after a lesson, sprinkle in some questions that cover learning from a few days, or even a few weeks ago.
• Brain dump: for 5 minutes at the start of a lesson, ask students to write down as much as they can remember about a specific topic or ideas from the previous day’s lesson.

I know many math teachers that structure entire courses in a way that has students revisiting and retrieving concepts throughout a semester. This practice, known as spiralling, is gaining lots of traction from Grades 1 to 12. The Ontario Ministry of Education provides a sample spiralled Grade 9 course plan to help teachers with planning their program in this way.

Move #7: Embed small-group intervention opportunities in every lesson

Even if a teacher implements moves 1 through 6 in their destreamed math class, there still may be students who need additional support in order to learn effectively. Some students with LDs enter Grade 9 having been given a modified curriculum in elementary school that was well below age/grade level. This gap in instruction and a lack of prerequisite learning may require the teacher to provide more intensive intervention.

Rather than putting the onus on students with disabilities to give up their lunch hours or after-school time to receive a teacher’s help, I recommend regularly carving out at least 15 minutes at the end of each lesson to work with one or more small groups of 3 to 5 students who need more intensive help and another opportunity to learn alongside the teacher.

Using formative assessment, create groups that have shown the same misconception or error, bring them together at a table to highlight their error, do some explicit teaching, and have students apply their new learning. Once students have their misconceptions corrected, they can go back to their seats, and you can work with another group. 

I want to reiterate that the formation of these groups is based on student work, rather than any special education label or history of prior achievement. These groups should be flexible and never fixed.

Summary

Mathematics classrooms can be enabling environments that remove barriers for students with learning disabilities, foster academic growth, and build students’ sense of self-efficacy. However, they can be disabling environments if students are not provided with the instructional support they require to meet their full potential. The 7 moves above are helpful starting points for destreamed math teachers to create the conditions within their classrooms to promote greater equity, inclusion, and academic excellence.

About the Author

Jason To serves as the Mathematics and Academic Pathways Coordinator for the Toronto District School Board, where he works with K-12 staff to tackle academic streaming and shift towards more equitable, inclusive, and culturally responsive teaching, particularly in mathematics. As a former high school math department head, he began challenging streaming in 2015 by eliminating Applied math classes and teaching inclusive Grade 9 Academic math, leading to significant gains for students, particularly for those with learning disabilities.

References

Roediger, H. L. III, & Butler, A. C. (2011). The critical role of retrieval practice in long-term retention. Trends in Cognitive Sciences, 15(1), 20–27. https://doi.org/10.1016/j.tics.2010.09.003