South Meridian Elementary

Although student understanding of mathematics at the same grade level varies widely, differentiating mathematics is relatively new. Generally, to differentiate instruction the following 3 elements are needed (Marion Small, Good Questions, Great Ways to Differentiate Mathematics, 2012):

• The focus of instruction is on the big ideas ensuring they are all addressed and understood
• An aspect of student choice is embedded whether through content, process, or product
• A form of pre-assessment must be done to determine where students are at in their learning

This year, teams of teachers in grade groups collaborated on an inquiry to differentiate mathematics in their classrooms using open questions and parallel tasks. These strategies are designed to meet the needs of students through differentiating instruction effectively. We undertook a book study together as a multi-grade group of teachers and read Marion Small's Good Questions, Great Ways to Differentiate Mathematics Instruction. Teachers created safe spaces in their classrooms for learners with a wide range of mathematical knowledge to actively participate in their mathematical communities with their peers.

Using the open questions strategy means the teacher is using one question with multiple access points for students to approach it through varying processes. This strategy allows for student growth even if the students are at differing stages in their mathematical development. 

In the example below, a grade 2 teacher posed an open question framed in such a way that a variety of responses or approaches are possible. This approach allows almost all students to posit a response based on their individual understanding - it is psychologically safer and fosters confidence.

 Most students can participate in the resulting discussion and the math talk is richer in the classroom. Math concepts can be seen from many perspectives and moves the students away from the narrow thinking that math is one question and one right answer. 

Grade group teachers in cohorts used Open Questions to develop and consolidate math concepts on a daily basis. Teachers provided open questions and parallel tasks for problem-solving at appropriate grade levels. 

For example, in grade 1, students use non-standard units to begin developing an understanding of measurement. They use non-standard units such as hands or feet to compare and order objects and relate the size of the unit to the number of units used to measure.  

In the task below students are using non-standard units of their choice (in this case, most students chose their feet) to measure distance across the classroom. When students went first one way and then another some noticed that it took the same number of their feet to cross the same distance there and back; others noticed that the number of feet was different for each student despite walking across the same tape lines. Others wondered if there was a better way to measure that made it "the same". The responses from students show the range of ways students answer and develop their mathematical understanding.  Students were able to see a myriad of possible solutions for problems and they were able to reflect and connect through math journals and the math talk communities built in their classrooms.

Teachers use mathematically meaningful parallel tasks such as the example above, that are purposefully slightly ambiguous in order to differentiate the problem. This allows for the engagement of students at all levels of numeracy development and helps everyone to experience success. 

Teachers reported increased student engagement with the open questions and parallel tasks. Using observation and anecdotal notes, teachers determined that the multi-accessible approaches created safe opportunities for students to participate and take risks in their mathematical development. Students who previously were reluctant to participate were able to offer their thinking and join in the math discussions without fear of being "wrong". The learning design was intentional and differentiated enough to draw students out and into the community of mathematicians.

Offering choices and having flexibility in the numeracy classroom set the stage for communities of learners that have positive mindsets regarding their mathematical abilities. Moving forward, teachers will continue to set the stage with open questions and parallel tasks but are ready to learn more about offering greater choice in math learning. We are moving our inquiry forward as we commit to learning how to teach with learning centres for math development. We are curious to learn how incorporating centres with skill practice, problem-solving, concrete materials, incorporating technology, and increasing writing opportunities will impact our learners..  We will follow our student cohorts throughout the year to determine how the addition of centres to numeracy impacts student outcomes. 

We want to create supportive equitable access for all of our learners to develop mathematical habits of mind. Being responsive to students' cultures, backgrounds, perspectives, and experiences requires that we address and acknowledge factors that contribute to outcomes among our students. Being responsive in our active differentiation of math instructional strategies is the start of this work. We want our students to experience high quality math instruction that is differentiated and accessible and holds high standards for all our learners. Attaining math proficiency for our students regardless of background, socioeconomics, culture, and gender is the goal that drives our work forward.