Thank you so much! We have been thrilled with the results thus far.

You're absolutely right--teachers generally think that showing incorrect examples will be harmful, especially for students who struggle with learning math.  However, we have published evidence that the incorrect examples may be even more helpful than the correct ones, and the low-achieving students benefit the most from the incorrect examples!

We draw on decades of research in cognitive science that have identified a variety of principles of processes that positively impact learning. In this case, we are combining the techniques of self-explanation, worked examples, and learning from errors to collectively benefit student learning in math. We actually did this work first in algebra classrooms and conducted a larger-scale RCT that showed positive results for students' conceptual understanding, procedural skills, and performance on released items from standardized tests. This work is published in the Journal of Education for Special Populations at Risk. I will try to figure out how to upload papers here for you! 

For the MathByExample project, we conducted an RCT with 5th grade last year and are finishing up the 4th grade RCT currently.  Results so far are promising!  Again, I will try to upload a brief writeup for you to view!

Unfortunately we are unable to upload additional attachments, but here are links to the two items Julie mentioned: 

AlgebraByExample Research published in JESPAR: https://serpinstitute.box.com/v/booth-jespar-2015

MathByExample brief write-up of preliminary analyses presented at NCTM in April 2018: https://serpinstitute.box.com/v/mbe-nctmproposa...

We're so glad you liked it!  One of the reasons we embarked on the MathByExample project was because many of the persistent misconceptions we were seeing in the Algebra students like issues with order of operations, properties of numbers, and fraction and decimal concepts and operations were really elementary school math content.  These types of misconceptions--perhaps especially those dealing with order of operations and fractions--are definitely problematic for students when they try to learn Algebra.  We've created the 4th and 5th grade materials to target these and other potential misconceptions earlier so that, hopefully, the students will not have these lingering problems in middle school and can focus on refining their knowledge of other concepts and procedures. 

Thanks for your comment! You're absolutely right - teachers have reported learning from these materials as well, both in terms of research-based practices and gaining insights to how their students are thinking through the mathematics. In the original partnership work, 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 materials that were easy to adopt, but fostered "learning-by-doing." The questions paired with the correct and incorrect examples are specifically targeted to untangle common misconceptions that students have. That being said, we will be developing a comprehensive MathByExample website for teachers to learn about the approach and how it can be beneficial for learning, similar to the AlgebraByExample website (http://math.serpmedia.org/algebra_by_example/). This website includes resources, such as a set of slides (http://math.serpmedia.org/algebra_by_example/sl...), which includes information about myths related to incorrect examples and student learning. 

Thanks for your comment! Our project has been focused on the development and testing of the assignments themselves, looking primarily at student outcomes. But with both the AlgebraByExample work and MathByExample work, several instructional leaders who work with the teachers using the assignments have reported that the assignments serve as a natural conversation starter for math team meetings. It is definitely something we will consider as we fully develop the website and provide resources and suggestions for use! 

That's great to hear! If you'd like to be notified as soon as the materials become available, you may join SERP's mailing list: http://serpinstitute.org/mailing-list.html We'd love to hear your feedback when you integrate it into your curriculum!

Thank you for your comment and for already sharing with your colleagues! We're thrilled to hear how relevant this work is to you and your students. We encourage you to reach out and let us know your experience with the materials next year! (info@serpinstitute.org)

Thank you for your questions!

As for teachers being apprehensive about showing students incorrect ways to solve a problem, that has certainly come up. Prior research has shown that the combination of incorrect and correct examples is more beneficial to students' learning than correct examples alone (Durkin & Rittle-Johnson, April 2009; Grosse & Renkl, 2004, 2007; Rittle-Johnson, 2006; Siegler, 2002; Siegler & Chen, 2008). But it's really important to explicitly mark/notate the example as correct or incorrect, and not ask or expect students to figure it out. In addition to the clear indication of incorrect work with the X, the presence of targeted questions that are directly related to the error eases hesitations. In fact, many of the teachers who have partnered with us as part of the research study have voluntarily expressed how they think the incorrect examples are actually more helpful than the correct examples! 

As for the AlgebraByExample workbook (and the soon-to-be released MathByExample workbooks), we definitely consider the assignments to be a supplemental resource. It can be used in addition to or instead of other practice worksheets as a do-now, exit ticket, classwork, etc. But we do not consider it to be comprehensive. Please let us know if you have other questions! 

Hi Katey--we've definitely heard teachers' apprehensions about showing incorrect work, and they are often particularly concerned about the lower-achieving students in their classes being harmed by working with incorrect examples. Because we wanted to be able to address these concerns directly, we have tested the impact of correct vs. incorrect examples (e.g., do they need the incorrect examples to learn, or are the correct ones enough) and investigated interactions between the effectiveness of the different types of examples and individual differences in student prior knowledge. Our research has shown that the incorrect examples are particularly beneficial, and that the benefit of incorrect examples is highest for students who struggle with learning math.  If you're interested, you can find the article here! https://www.researchgate.net/publication/301759...

Hi Mari!  The worked examples themselves need to be clearly marked as correct or incorrect, and should each target a single concept or misconception. But the bigger surprises were in what matters for the accompanying self-explanation prompts. Many people's instincts are to just ask what was right or what was wrong, and have them fix the wrong answers. Instead, we focus the self-explanation prompts on the particular features of the problem that are relevant to the target concept or misconception. The key is to get learners to notice the components of the problem that make the shown procedure right or wrong, to think about the meaning of that feature in the problem, and to force them to confront common misconceptions about those features. Even if a student doesn't hold that particular misconception themselves, they can still learn quite a bit from refining their thinking about that feature. 

Would love to hear more about your efforts with little kids!  I was on a dissertation committee recently where the student tied this approach to debugging in college-level intro computer science. My sense is that with coding you do need to let them do the correction as well, but that it would be good to have them think critically about the conceptual features first.