Stretching in Math Class

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This post has been marinating for a while and I’ve been waiting to write it up.   State testing is just around the corner and I feel like this is a good time to press send.

One huge emphasis that I see in schools is related to the idea of student growth.  This is communicated in schools, during teacher pd meetings, when talking about Hattie’s next best effect-size list and can even be part of teacher evaluation criteria.  I see this when school districts use MAP, state testing, or a similar type of tool that measures growth over time.

Schools, teachers, and parents want students to grow.  In schools the focus of growth primarily related to academic content.  How is that measured?  Well that depends on the teacher/district/organization.  Some teachers go the route of using a pre vs. post-test.  Others give multiple formative checkpoints and then use them along with student reflection components to show growth on the summative.  Case in point – there are multiple methods to show student learning and growth.

Here’s my not so small gripe.  In an effort to show growth some educators may feel rushed to “get through” as much content as possible.  I hear this a lot more in math classes than other content areas at the elementary level.  Math has a subjective linear vibe that I think some teachers hold onto. This idea is often reinforced through the structure of some of the adaptive standardized tests that communicate math growth to teachers and school administrators.  This can be a bit troublesome if these types of tests are used for evaluation purposes as it brings along additional pressure.

I find students make meaningful math connections when they’re given time to process and apply information.  I believe rushing through concepts or stretching to just expose students to higher-level concepts that aren’t part of the lesson isn’t as beneficial as it seems.  Moving off the pacing guide or lesson to stretch to other concepts might not be the best idea. When I first started teaching I remember having a teacher talk about exposure all the time.  The teacher would say, “If they’re just exposed… then they’ll complete those problems correct and that’ll push them to the next concept.”  This teacher was truly amazing (and made some great coffee in the mornings), but I questioned this then and still do now.  If we’re exposing students to math concepts so they’ll score well on an adaptive test then that’s another issue altogether.

If a lesson is looked through a linear math lens a teacher might feel as though they should introduce fraction multiplication if students are doing really well with multiplying whole numbers.  Is that the right move?  Should a teacher stray from the lesson plan to possibly reach a few kids that seem like they’re ready?  I’m not saying yes or no because it depends on the station and students, but I’m more in the no camp.  Stretching math concepts in a lesson/task for exposure sake doesn’t last.

Last summer I was able to reading Making It Stick and came away with some applicable ideas related to changing my study guides and how retrieval practice benefits those wanting to learn.  I find that there’s sometimes pressure to stretch to another concept for exposure sake.  Instead of stretching concepts, there should be opportunities for students to enrich their understanding through connections.  This looks different and is more challenging in my opinion than just pressing the accelerate button temporarily.  I believe that taking time for students to process, reflect and engage in meaningful math tasks will last more than a glimpse optimistic exposure that may soon be forgotten.

Putting it all Together

Building solid roots of retention
Building solid roots of retention

Last week I had the opportunity to finish up a book study on how the brain learns mathematics.  During our last GHO the crew discussed the implications and takeaways from the book.  We had instances of affirmation and some of the research had us look at our instruction through a different lens.  In my mind this was perfect timing as school is just around the bend or has even started for some. The last chapter in the book discusses the need to connect brain research and how educators teach mathematics.  Moving forward there are few different questions I want to consider while planning.


Is the lesson memory compatible?

Basically, are the number of items in a lesson objective too much, too little, or just right?  At some point I feel like all students need transitions.  Being aware of when to transition comes with teacher experience, but breaking up that time block dedicated to math instruction is important.  After the transition students’ working memory has an opportunity to refresh.  I couldn’t stand 60 minutes lectures when I was younger and still can’t today.  The brain needs time to move items into it’s working memory.

Does the lesson have some type of cognitive opening?

According to Sousa’s research, the degree of retention is highest during the first 10-20 minutes. New material should be taught after students’ are focused on the lesson. The opening of the lesson should provide students with opportunities to see new information and correct examples.  I feel like many teachers ask questions about the new topic to get student input and to make curricular connections.  This isn’t always the best option because students may reference incorrect information or examples and students will most likely remember that.  Instead the lessons should emphasize correct information in some type of mini-lesson format.  This was a bit surprising for me because I can’t count the amount of lessons that I’ve started by using some type of KWL activity.

Does the lesson have some type of cognitive closure?

Sousa also concludes the teachers should initiate some type of cognitive closure. This can take on many different forms.  During closure students participate in mentally rehearsing and finding meaning of the topic discussed in class.  There’s a difference between review and closure.  I’ve always put the two words in the same realm.  When teachers review they’re doing most of the work.  Closure is designed so that students do the majority of the work.  Closure doesn’t necessarily have to happen at the end of class.  Procedural closure can be used to transition from one activity to another, while terminal closure ties the day’s learning together.

How can I incorporate more writing in math class?

I’ve used math reflection journals before and I think there’s so much potential in having students write about their math experiences. Sousa believes that incorporating writing in math can be an effective way for students to make meaning of what they’re learning. Foldables and Interactive Notebooks have been the rage for the past few years but I’ve always questioned their effectiveness.  Students shouldn’t be rewriting the textbook or journal.  Students should use their own thoughts and vocabulary in their writing. Students are making sense and connections to the math concepts by writing about them. By writing down their math experiences, students are participating in elaborate rehearsal of newly learned concepts.  In addition, the writing can be used to show individual student growth over time.


Moving forward I think all of these questions have me thinking about how lessons are planned. I fell like all of them play a role in how well students retain information. All in all, I think there’s a balance in how teachers plan their individual lessons.  Retaining information is important, but students should also be given the opportunity to explore and build  a conceptual understanding of topics.  Retaining those experiences are pivotal throughout the year as concepts are built upon one another.  Being aware of how the brain learns math can help in that planning process.  I feel like being more intentional and using a critical eye in how I organize my class benefits how my students understand math.  To me this process of planning is more of a journey and not necessarily a solution.