I teach algebra. I also teach calculus. And I can tell you that the majority of the mistakes that my students make in calculus have nothing to do with finding a derivative or integrating, it is all about algebra.

– Linda Kadingo, Green Bay

The example-based problems really get the kids talking to each other. If there's some stubborn misconception, they can be so convinced sometimes that they are right on a wrong idea. When you show them the problem that is correctly done and they think, "Wait a minute that's not correctly done.” They'll try to point out to you, "Hey there is something wrong with this—this is not actually correctly done." And you just have to keep saying, "No that is right, you need to try and understand what is it that you're not seeing." It's gotten the kids talking more to each other, and it has definitely gotten me talking to the kids more.

– Paula Zelinski, Evanston

Students don't realize that there are a number of misconceptions they have in algebra. When they actually have to have a conversation about what that fictional student did right or wrong, it kind of unearths the misunderstanding and shows that it’s the kind of thing that many people can get wrong.

– Anthony Lauer, Ann Arbor

Changing classroom practice can be extremely difficult. But the first step I think is important is having something that a teacher really believes is worth trying to use. I have yet to meet a teacher that will not try and apply something new if you do the legwork for them and show them that something will impact their instruction and help their students. So I think finding that AlgebraByExample is working for students who typically struggle, and then giving teachers the understanding and the tools to do something differently in the classroom is extremely valuable.

– Randy Yates, Shaker Heights

It led to student discussion about problems, a common language of solving correct and incorrect solution methods. It also lowers the avoidance and resistance to get started on problems, since they were required to make judgment on work and assess rather than create.

– Kelly Rooney, Evanston

These assignments are a window into students’ thinking and it is really eye-opening for me to see that there is a misconception and then I can see that the probing questions help students really get involved with that misconception and work to fix it.

– Katie Myers, Evanston

The example-based assignments have inspired many teachers of Algebra 1 to start using error analysis in the classroom, as well as formative assessment.

– Stacey Zimmerman, Madison

This approach is very similar to critiquing the work of peers, but the great thing is that it is done with a fictitious student. You feel comfortable making a critique of what a fictitious student has done where it can be a non-starter if you have to critique a peer.

– Anthony Lauer, Ann Arbor

When I listen to my students talking about regular assignments, they ask each other “what did you get?”. But when they talk about AlgebraByExample assignments they ask “why did you do that?”

– Katie Myers, Evanston

In most of our workbooks or textbooks there are only problems. There's no starting point for students. If they don't know how to start it, they don't do it. There's no discussion that happens. They have nothing to go from if they're totally lost. The AlgebraByExample worksheets—they start out with something for students to edit and it helps to start the conversation. Putting the example next to a similar practice problem on a worksheet really helps students to connect the ideas together and apply them.

– Anthony Lauer, Ann Arbor

I find that both the correct examples and incorrect examples help kids identify themselves with somebody else easily. [With misconceptions], kids can be really stubborn, and they really don’t believe you that it’s wrong. To see a kid look at an incorrect example and say, “no, but this is correct,” and then they kind of have that moment of “oh, I really was off, and now I understand it more.” I think they are allowed to engage with that kind of example/problem pair more so than if it was just a standard practice problem.

– Katie Myers, Evanston

One of the best things about AlgebraByExample is that it's not a new curriculum, not a completely new idea. You don’t have to change the books you use or the way you teach. You're working it into your current lessons. It can serve as extra practice, as a review, and you just make it part of your lesson.

– Anthony Lauer, Ann Arbor

The idea of having students critique other students' work and analyze their solutions - whether they're correct or incorrect solutions - is extremely valuable for students learning algebra.

– Jeff Ziegler, Madison

Telling the students this is incorrect forces them to say, “Well, that's what I do! What should I do if I'm doing the same thing as this boy in this problem? What's wrong with what he did?” And if they're not sure of the reasoning, they can have a partner or group that they can discuss things with. A student might say “That’s the mistake I made in my homework last night” . . . and it starts the conversation.

– Ellen Hopkins, Ann Arbor

Development of AlgebraByExample was led by Julie Booth (Temple University) through a SERP collaboration with the Minority Student Achievement Network (MSAN). The SERP-MSAN partnership has been supported to conduct this work by The Goldman Sachs Foundation and by the Institute of Education Sciences, U.S. Department of Education, through Grant R305A100150 to Strategic Education Research Partnership Institute. The information provided does not represent views of the funders.

The AlgebraByExample Team

AlgebraByExample by SERP is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.