# The Landscape Of Math Education: Fostering Student Understanding

As important as it is for teachers to have a full understanding of the progression of mathematical ideas, it is also helpful for students as well.

There is often a disconnect for students in the math classroom, but this disconnect doesn’t always come from the content in front of them. Students approach writing in math class with little recollection of how they are taught to write in ELA or SS. More dangerously, students approach math class with little recollection of what they learned in previous years. Some of this is because it wasn’t retained over summer vacation, some is because they never fully grasped it before, but a lot of it is also because we don’t help them see the content as fluid and developing from year to year.

Although students are introduced to fractions in third grade, it often seems like they have never heard of a fraction upon entering sixth grade. Students have become accustomed to “learning” something, passing a test, and being able to forget about it. We need to help them see that the ideas in mathematics are not separate entities – that they build on themselves with complexity. However, telling students “you’re going to need to know this next year” risks alienating students if they are struggling with a topic.

Instead, it is our job to help them see how the different topics they have learned deepen from year to year. One way to do this is in spiraled review, but not just problems students have seen and mastered in the past. Begin with part of a problem, something most students will be familiar with and ask them to identify how it is familiar. Once students can recognize something in the problem, have them talk about things they know (even if it isn’t totally relevant to the problem at hand). For example, in solving percent of a quantity problems, students may talk about decimals, place value, addition, multiplication, ratios or fractions. Pamela Weber Harris uses the saying “Math is figure-out-able”. She encourages students to start with something they know and work from there. This helps students connect their prior knowledge to something that they are learning.

Get students out of the habit of always starting a problem by asking themselves “what’s the answer”. One great resource for problems that help students develop the mathematics behind a problem is Dan Meyer’s Three-Act Task Spreadsheet.

These three act tasks put students in charge of identifying the mathematics within the situation. Instead of asking “what’s the answer”, students must first figure out what the question is, what information is needed, and how to answer their question.

Another way to help students identify the mathematics that may be present in the problem is using a problem-solving template. By asking students to get accustomed to understanding what mathematical content they are using, they are more likely to see that the content is often similar and very related year to year.

Elizabeth Masalsky is a 6th, 7th, and 8th grade mathematics teacher at Battery Park City School in Manhattan. She has a post-baccalaureate in mathematics from Brandeis University and her master’s in secondary math education from Bard College. Elizabeth is a Math for America Master Teacher and continues her professional development through workshops with Math for America, Metamorphosis and Math in the City.