A few months ago I remember sitting in a meeting where teachers were discussing students and their math placements. The conversation revolved around the topic of whether students should change math placements for the next school year. For example, should a student stay in a homeroom math class or be part of an accelerated class? How will we provide additional math support for particular students? These types of questions tend to occur throughout the school year, but action for the next year often takes place near the end of the school year.

The decision to change placements is based on a variety of factors, but many schools/districts narrow down their criteria using standardized assessment data. That data is often in the form of achievement, cognitive, and/or even aptitude tests. Each district that I’ve been in has had a different process to determine subject placements. This placement process becomes even more apparent as students travel from elementary to middle or middle to high school. Students’ birthdates, norm-referenced test scores, and percentages often take center stage during these decisions. Sometimes the conversation evolves into whether students would be able to transfer the skills to a more rigorous math program than the one that they’re currently attending. The conversations are usually productive and emphasize how to best meet the needs of students.

The topic of exposure is often brought up when making these types of math placement decisions. A quick Google search will bring up one of the definitions – “introduce someone to a subject or area of knowledge.” I have heard on more than one occasion the following paraphrased statements/ideas:

- If students haven’t been exposed to the content then they won’t be prepared
- Those students weren’t exposed to above grade level work so they won’t be ready for that class
- The reason the student scored at the ___%ile was because he/she was exposed to that skill before the test
- If they’re not exposed to this class then they won’t take higher-level classes in high school

I feel like these types of phrases are thrown around lightly and in a way that doesn’t hit at a bigger issue Being exposed to content doesn’t necessarily equate to applying it in different situations. Showing a students how to complete a specific skill/process doesn’t mean that they fully understand a particular concept. Students might understand a process, but are limited during the application stage. Also, educators need to keep in mind whether an above grade level curriculum is developmentally appropriate for students.

I believe the bigger issue here is equity.

- Are all students receiving high-quality math instruction?
- Do the tasks and math routines allow students opportunities to explore mathematics and build solid understandings?
- Do students need enrichment opportunities instead of acceleration?
- Will being exposed to a new curriculum/topic/grade-level be the panacea to move students to a higher math placement? Is that even a goal?

So many questions are above and I’ll admit that I don’t have a solid solution for them. I think we have to go back to what a school/district values. I do know that I want students to be curious about math and dive into its complexities. Classrooms should develop a culture where taking mathematical risks is the norm. High-quality math instruction takes investment from a school and district. Ensuring that this instruction is occurring and support is provided is also important. Mathematical tasks that encourage students to observe, create, and apply their understanding beats limited exposure any day. Exposure is the first step and it doesn’t end there.

Generally the best practice on a per child basis is enrichment and acceleration. The two aren’t a dichotomy. Then if you can answer yes to your first question “Are all children receiving high quality instruction?” I think you’ll still find that the curriculum doesn’t work as well for everyone. That’s always been the reality on the ground in classrooms that’s driven the need/desire for acceleration. There are practical limits to the bandwidth of an individual teacher and how much differentiated activity can occur within one classroom. You reach points where the cons of continuing to stay at level outweigh the benefits.

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Hi Benjamin, I find that there’s a need to accelerate in certain circumstances. The bandwidth limit that you describe is realistic (I’ve been there) as teachers continually attempt to meet the needs and differentiate. Pulling resources from a grade level or more above the current standards can be challenging and might not necessarily be appropriate. There’s a point where students end up having an independent study or in some instances they’re just being exposed to content. I’m in agreement with “… where the cons continuing to stay at level outweighs the benefits” but I find that some schools/districts move to acceleration as the first step. Thanks for sharing your thoughts!

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