One of the most common questions we hear from math teachers is “Where can I find good problems for my students?”. There are more than a dozen sites reviewed on CollectEdNY that answer that question but we are really excited to share MathMemos which, like CollectEdNY, is entirely focused on adult education math teachers and students.
MathMemos: The Basics
At the heart of every great math class, there is a great math problem. MathMemos is a way to enter into the classrooms of our peers and the minds of adult numeracy students.
- The goal of the site is to support teachers and give them tools to teach open-ended math problems to adult education students.
- Every MathMemo consists of a problem, samples of student work, and a teacher write-up in which adult education teachers describe their planning, their students’ work, and their reflections after using the problem with students. They also include practical suggestions for bringing the problems to life in the classroom.
- MathMemos has downloadable pdf and word docs of each problem, so teachers can have ready-to-go handouts, or make changes to the problem to suit their own students.
- Samples of student work are also available for download as either a pdf or word document. The student work for each MathMemo reflects a range of student strategies that teachers found interesting, with some commentary from the author about why they wanted to share it.
- MathMemos can be searched by broad content areas (Algebra, Functions, Geometry, Number & Quantity, Statistics & Probability). Teachers can also search by tags referring to specific problem solving strategies (i.e. charts and tables, guess and check, creating equations, visual strategies, etc) or topics within content areas (i.e. equality, fractions, solving equations, system of equations, visual patterns, etc). All of the search options can be found on the right side of the MathMemos homepage.
- The intended flow might go something like this: Choose a MathMemos problem and try solving it for yourself. Then look at the student work and see what you notice. Next, read the teacher write-up. If you have any questions, write them in the comment section below the teacher write-up. Then, try the problem in your class and share your experience in the comment section. If you can, try to work with another teacher.
Can adult education students really solve problems like these?
All of the student work that accompanies each problem comes from real adult education students. What you will notice as you look through the student work is the wide range of creativity that students bring to problem-solving when they are given the encouragement and support to develop their own problem-solving strategies. The problems on MathMemos are all chosen because they have what we call a low entry point and a high ceiling. They are challenging, but they are accessible to a wide range of students – something that works very well in the mixed-level math classes that we all teach. Most important, the problems can each be solved using a wide-range of problem-solving strategies, from creating visual representations, making charts, guess-and-check to setting up equations.
Seeing the student work will not only give teachers confidence that their students can work on these problems, but also give them a window into how their students might approach the problem, where they might get stuck, and how to help them persevere. The problems also require students to use their background knowledge, but almost none of them require students to have any particular background knowledge. That is to say, problems can be used to deepen understanding during a unit you are teaching, but they can also be used to introduce a topic, before students have learned any specific content.
I’m interested, but I’m not sure how to teach by giving students problems before teaching them how to solve it. How does that work?
To get started, take some time to solve the problem yourself, trying as many strategies as you can think of. Then think about the challenges your students will have and come up with questions you could ask them to keep them going but not give too much away. Then think about which student strategies we might want to focus on and talk about in a whole-class discussion. All of this can be a little intimidating when you are first trying it out, which is why MathMemos is such an exciting resource. Teachers in the field have already done these steps, and their experiences and reflections will support you in teaching these problems.
How can MathMemos help me teach?
MathMemos contributors are all adult educators who are passionate about teaching math content through problem-solving activities. They have written their MathMemos in order to reflect on and improve their own math instruction. Their experience gives them the opportunity to learn from their students’ thinking and, in turn, grow as teachers. And by learning from their experiences and analyzing the samples of student work that they shared, we can too.
Taking the time to reflect on teaching and learning is a key factor in our growth as teachers, but the life of an adult educator does not always give us the breathing room to think about what went well and where there is room to improve after each class we teach. MathMemos is a way to help. To paraphrase the Reflective Teaching chapter in the CUNY HSE Math Curriculum Framework, we are all scientists looking into how students learn and solve problems. MathMemos is one way for teachers to share their findings with other teachers.
In addition to helping with individual problems, the contributors sometimes make observations that have interesting implications for teaching in general. For example, Daphne McKnight wrote a MathMemo called Chickens and Goats where she shares her experiences using the same problem in a low-level Basic Education class and an upper-level HSE class. What she found is that both groups were equally engaged with the problem and had similar challenges and successes. That observation suggests that using problems like Chickens and Goats really can support math students at both ends of the spectrum in a mixed-level class.
How do the problems on MathMemos help prepare our students for the TASC?
A big thing that students will learn from working on these problems is perseverance.
Students are often of the mindset that every math problem has one right way to solve and that way must be memorized and then implemented at the proper time. The problem with that kind of thinking is that when students are confronted by a problem that is unfamiliar, they think they cannot answer it and they shut down. We need to help our students believe that they can solve any problem, even if it looks like something they haven’t seen before. In order for that to take place, a few things need to happen. For one, students need to have several experiences in which they struggled with a challenging math problem, didn’t give up, and had their effort rewarded by coming to a new, deeper understanding of the underlying mathematics and the creative problem-solving strategies that helped them and their peers solve it. Students also need to practice trying different problem-solving strategies, so they can choose and use them more efficiently.
Teaching isn’t one size fits all and it is not about filling empty buckets. If it were, we’d all be replaced by workbooks and computers. We need to build from where our students are to get them to where they need to be.
Research tells us that knowledge is built from the concrete to the abstract. The problems on MathMemos can be used to draw out student thinking and bring a wide range of concrete or representational solutions (drawing pictures, acting it out, making models, etc). The write-ups can help teachers use those solution methods as the foundation to introduce more abstract and formal mathematics.
Write Your Own MathMemo
MathMemos is a living site. We will continue to add new problems and write-ups. In addition to enjoying the benefit of what other teachers share, MathMemos encourages any adult education teacher to submit their own MathMemo as an exercise in self-reflection and professional growth and to allow their work and students to help improve math instruction for our entire field.
I strongly recommend teachers visit MathMemos – a sister site of CollectEdNY – dedicated to improving adult literacy math education one great problem at a time