Blog

by Joshua A. Taton, Ph.D. | September 28, 2023 | 5 min read

The advantages far outweigh the disadvantages, when supporting teachers in using a well-designed curriculum program in mathematics.

The disadvantages? Curriculum programs offer far too much and far too little, paraphrasing a well-known observation from researcher Ben-Peretz (1990).

In other words, they can’t possibly offer enough information to guide a teacher’s every decision, particularly given that classrooms are their own unique ecologies. And they also offer far too much information—especially modern programs that offer teachers options for adjustment, resources for differentiation, technology add-ons, notes on mathematics concepts, and guidance on research-based pedagogy.

The advantages? Basically, they are the same as the disadvantages.

Curriculum programs enhance coherence, help teachers focus on core content (when there’s already too much to cover), elevate rigor and provide opportunities for application, provide scaffolding and differentiation support, and—research shows—can help teachers deepen their understanding of the mathematical concepts and procedures, as well as offer research-based pedagogical strategies. They also provide aligned assessments, in many cases, and—as anyone who has been involved with the laborious task of designing valid and reliable assessments knows—this requires a LOT of prior knowledge and skill and teamwork.

And, to me, what makes the advantages more valuable than the disadvantages is: without well-designed materials, teachers have multiple jobs in one—curriculum writer, field-tester, assessment writer and field-tester, instructional planner, and more.

So how do we square this circle?

• • By showing teachers, and school leaders, that well-designed curriculum materials are NOT scripts.

  • By showing them that they provide guidance and suggestions and options, based on research and field-testing.

  • By showing them that the best teachers in the world, from top-performing nations, spend hours of time discussing, studying, and planning WITH curriculum materials alongside their colleagues. (Everywhere I’ve gone, when an under-resourced system invests in this—and coaching—the results are immediate; test scores stop declining and improve WITHIN one year.)

  • By showing them that curriculum materials help reduce the decisions they need to make, and that materials offer them a framework for making some of the millions of decisions that are needed each day.

  • By showing them how to make REASONABLE decisions WITH curriculum materials and how to AVOID unreasonable decisions with materials.

What are some reasonable decisions or adjustments for teachers to make, when using well-designed curriculum programs?

1. Skipping “pre-req” lessons and “extension” lessons that are above or below a given grade-level

2. Consolidating repetition, if students *clearly* understand

3. Adjusting warmup activities and cooldowns (or exit tickets) to meet students’ needs and the taught lesson

4. Changing the context of problems, as long as all the students can still understand, but not the mathematics

5. Adjusting the scaffolding, providing ELL support, utilizing differentiation options

6. Selecting from among several parallel options for activities

7. Adjusting problem-sets (practice problems)

8. Presenting the content and asking students to “predict the problem”

9. Asking students what the units should be for the final answer

10. Offering sentence frames

11. Doing QUICK numeracy or reasoning routines (e.g., number talks, dot talks, "estimation180" activities, "which one doesn’t belong" discussions, "visualpatterns" investigations, splat, guess the number or pico-bagel-fermi games, SolveMe Mobiles)

12. - Changing a problem to a three-act math problem (or similar)

What are some unreasonable decisions or adjustments? (These are deemed unreasonable, because they disrupt the intended design of programs and, therefore, limit the research-based effectiveness of the program.)

1. Changing the sequence of lessons and units

2. Changing the level of rigor without making thoughtful adjustments to scaffolding

3. Skipping major content lessons or units

4. Skipping conceptual problems or fluency practice

5. Ignoring guidance on concept-building activities

6. Not doing checks for understanding

7. Ignoring differentiation support, assuming students in every classroom need some and will benefit

8. Not planning with materials

9. Not collaborating with colleagues to keep relative pace

10. Stretching lessons over many extra days

11. Not providing rigorous instruction EVERY day

12. Designing assessments from scratch

We should be coaching and supporting each other in how to make and reflect on these decisions.

I welcome your thoughts!

Need Help?

I am ready, willing, and able to help your school or system adopt research-based changes to your assessment practices. If you want to see deep and meaningful change, including renewed excitement about mathematics instruction, in your building(s), please contact me for a consultation.