The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. One of these practices is to make sense of problems and persevere in solving them. Often, students can memorize multiplication facts such as 9 ÷ 3 = 3 but they wouldn’t be able to explain why or how they got 3 as the quotient. Some students can also add, subtract, multiply, and divide really well but when presented with word problems, they wouldn’t know which mathematical operation to use. So, how can we help students understand math deeper and equip them with, not just facts, but the ability to apply mathematical understanding when solving problems?
According to PNA’s Math program, Bridges, in third grade, students are expected to know that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the meaning of a problem and look for ways to solve it. Third graders may use concrete objects or pictures to help them conceptualize and solve problems. They may check their thinking by asking themselves, “Does this make sense?” They listen to the strategies of others and will try different approaches. They often will use another method to check their answers.
In third grade, students are given lots of opportunities to learn how to explain their mathematical thinking, reflecting on how and why they used specific steps or strategies to solve a problem.