Hello Susan,

Thanks for your message! We encourage teachers to use the assignments as they would any other assignment in their class. Some have students work on them independently, while others ask students to work with others. We find both to be effective. Teachers have generally noted a preference for students to complete the assignments in pairs and groups, since the self-explanation questions naturally prompt student-student discussions and can be a great starting point for mathematically-rich whole class discussions as well. Even if working independently, students are engaging in critiquing the reasoning of others since they are analyzing and responding to prompts about a fictitious student’s work.

While some of our assignments focus on procedural knowledge, we strive to mainly target conceptual understanding. In other words, we focus more on the “why,” rather than on the “what” or “how.”  Some of our assignments do target magnitude and other do focus on estimating reasonable answers. Finally, we strive to support multiple strategies throughout the set of assignments. For instance, we demonstrate the standard algorithm, as well a various models/representations used in the range of CCSS-M aligned curricula our partner districts have adopted. To get a sense of the range of concepts we target with the assignments, it is helpful to look at the full set of assignments for each topic. You can check out the various assignments on the website: https://math.serpmedia.org/math_by_example/

Hi Denise! Thanks for your comment. You’re right, “My Favorite No” definitely seems like a similar strategy for banishing the stigma around errors and getting students to tune in to particular features of the problem and shift away from answer-getting! In terms of data collection, our work focused primarily on performance outcomes. However, we did include pre- and post- surveys, and included expectancy and value items, as well as items about the error climate of the classroom. These items asked students to indicate how errors are used in their math classrooms and how they feel about the use of errors. We anticipate that the MBE assignments may increase students’ perceptions of the functionality of errors as a learning tool in the classroom. These data are still being coded and analyzed.

Hi Bruce! It would be great if you shared this with your colleagues -- we think this would be a great tool, especially for new teachers, since it allows teachers to gain insights into students’ thinking about these key mathematical concepts. You can access the full set of assignments on the website: https://math.serpmedia.org/math_by_example/

As for higher-level mathematics, we actually started this work in Algebra 1, developing and testing AlgebraByExample. It was with AlgebraByExample that we found significant results for students’ procedural and conceptual understanding, with greater gains for students at the lower end of the performance distribution. The full set of these assignments can be found on the website: https://math.serpmedia.org/algebra_by_example/ For more information about the background of the project, please visit: https://math.serpmedia.org/algebra_by_example/the_r-d.html We have also applied for funding to expand to high school Geometry content–GeometryByExample.

Hi Bruce and Allie!  

I was tangentially involved with the AlgebraByExample work a few years ago.  I have recently taught undergraduate mathematics, and I have thought a lot about how these materials could apply in a higher education setting as well!  I think it would be an excellent way to address the misconceptions that continue to appear in undergraduate math classrooms.  I am so glad to hear that there are plans for GeometryByExample!  This is great work!

Hello Mahtob, Thank you for your comment. Our assignments utilize a wide variety strategies, including models and graphs. The assignments also align to all CCSS-M standards for 4th and 5th grade, including geometry and measurement. To get a sense of the range of strategies and topics, it is helpful to look at the full set of assignments. You can check them out on the website: https://math.serpmedia.org/math_by_example/

In addition, prior to MathByExample, we designed a similar set of assignments focused on Algebra I. They can be accessed on the website: https://math.serpmedia.org/algebra_by_example/

For more information about the background of the project, please visit: https://math.serpmedia.org/algebra_by_example/the_r-d.html

Please let us know if this doesn't answer your question, we'd be happy to elaborate further! 

Thank you so much for sharing these resources!

Hi Beth! Great to hear from you here! In the original partnership work that led to the development of AlgebraByExample and then later MathByExample, one of the constraints district leaders put on the design of the approach was to not require professional development and training in order to adopt the materials, so we had to strategically design “light-touch” materials that were easy to adopt and fostered "learning-by-doing." And many teachers have reported exactly that -- they reported learning from these materials both in terms of research-based practices and gaining insights to how their students are thinking through the mathematics. So in the pilot conducted with both “ByExample” resources, no professional learning was conducted with teachers. We have, however, hosted some meetings with teachers who were part of the development team to review the theory behind worked examples, self-explanation, and dos and don’ts for creating your own worked examples, so the project team has discussed the possibility of creating professional learning sessions around these topics for dissemination as well. For example, my colleagues also authored “A Worked Example for Creating Worked Examples” that can be used as a resource, linked here: https://www.researchgate.net/publication/281066179_A_Worked_Example_for_Creating_Worked_Examples

As you mention, there is also the possibility of providing guidance to teachers on giving students feedback and on utilizing data to make decisions about future learning. In many cases, because this is meant as a supplemental resource and not a comprehensive curriculum, we’ve had pushback to add “one more thing”, since extensive professional learning and guidance is often a requirement of the core curriculum and is given priority by districts. So, to date, this hasn’t been on the radar, but we are certainly open to the possibility as we continue to explore how we can further support teachers and districts in adopting and implementing the assignments. I’ll definitely be in touch with you as we think more about it to see whether it aligns to what you are imagining would be helpful.

As for results, we are still combing through data and entering all correct/incorrect/completion data from the workbooks, and we won’t have final results until that work is done. But preliminary analyses are showing that even without taking individual assignment completion into account, 5th grade MathByExample students improved their procedural knowledge and conceptual understanding more than peers who only completed problems to solve (identical problem sets, but without the worked examples and prompts). I will send along more details once we have more refined results to report!

Thanks for sharing Allie. I look forward to hearing from you soon. I am always open to finding ways to support teachers so when we touch base lets discuss that further. 

Hi Kathryn! SERP’s focus is on K-12, but we have heard of the AlgebraByExample materials being used at the community college level. If you decide to try out the materials with your students, please let us know how it goes! Perhaps there is also an opportunity to create additional worked example assignments that align to your content as well. I’ve pasted some resources below:

AlgebraByExample website: https://math.serpmedia.org/algebra_by_example/

“A Worked Example for Creating Worked Examples”: https://www.researchgate.net/publication/281066179_A_Worked_Example_for_Creating_Worked_Examples

Lizhen - Thanks for your comment! The prompts on the page are actually intended to be written responses, but when done in pairs or groups, they naturally prompt discussion between students. Some students may not recognize what Zach forgot to do when multiplying 316 by 3 and different students may have different strategies for knowing whether an answer is unreasonable, for example. By having students complete the items in pairs or groups, it is not uncommon for a comparison of potential responses to lead to a discussion about the content of the example.  

Our primary research focus was whether these assignments were more effective than traditional assignments with only problems to solve relating to students’ academic performance. We did not specifically study language use in discussions formally; only noting how the assignments were generally administered (e.g., independently, in pairs) and noting student utterances during observations to help inform revisions. It would certainly be an interesting extension of a future study, however, to look more carefully at the types of discussions students were having and how they varied with the different types of prompts as well!

Interestingly, for a dissertation, a colleague did an analysis of the formality of the language used in the AlgebraByExample written responses. We looked for differences in learning based on whether students used the formal language (i.e., coefficient) or informal language (i.e., number next to the x). We found that the type of language used did not affect students’ learning. As long as students attempted to explain their reasoning (regardless of the type of language used), they benefited from the AlgebraByExample assignments.  See https://www.researchgate.net/publication/326714919_Precise_mathematics_communication_The_use_of_formal_and_informal_language for more details.