True Confession: I am mathematically challenged. Throughout elementary school, I excelled in all areas of Language Arts, but I struggled in math (especially with word problems, oddly enough). Struggling in elementary school led to struggles in middle school, and I was finally able to work through some of my issues in high school. But I think I’ve finally figured out what I lack: conceptual understanding of mathematics.
In other words, I have no number sense.
Teaching Number Sense
Conceptual understanding of mathematics, or number sense, is the foundation of mathematical understanding. Without number sense, students struggle learning the basic facts, and that translates into failing grades when they enter middle school and they are expected to be able to perform complex operations in their mathematics classes. Worse, it limits what students can do after their formal schooling ends.
Number sense isn’t something that is always taught explicitly. It’s embedded. But rather than teaching early elementary students how to do double-digit subtraction using a standard algorithm (bigger bottom, better borrow!) we need to be teaching them how to decompose numbers, start to think relationally, and do these kinds of problems in their heads or by using strategies that make sense to them. As students’ ability to think flexibly about numbers grows, so will their ability to perform more complex operations.
How Sums Stacker Works
Sums Stacker is a great app for supporting the development of number sense. There are different levels, (easy and hard), different modes (solve, infinity, and timed race modes), and different graphic representations of numbers (including numbers in different languages, money, shapes, fractions, and more). There are three columns, and students must make the sum of the dice, fingers, etc. match the number that gets shown on the column. If the student stacks the sum correctly, the items dance and a little jingle plays, and the numbers on the columns reset so the student can play some more. In an effort to help students think carefully and not guess, there is a running ratio of moves to points. The lower the ratio, the better.
I find that the app is best suited toward the younger elementary students— Kindergarten through third grade— but it can be beneficial for all learners of mathematics. It offers a great opportunity to practice for upper-elementary students (and anyone else who needs a little practice… ahem).
Common Core Connection
According to the Common Core State Standards in Mathematics, students aren’t supposed to start using the standard algorithms until fourth grade. This means that the primary grades can really focus on the conceptual understandings and allow students to represent problems in their own ways. Some have argued that this is “dumbing down” the curriculum. I disagree. I think it allows children to develop a strong understanding of numbers before being forced to do an algorithm that they don’t fully grasp.
Common Core Mathematics is organized differently than language arts. So, to be as specific as possible, Sums Stacker helps students develop their skills in Operations and Algebraic Thinking (CCSS OA.A), which helps them master the skills they will need to understand and ultimately master standard algorithms as they progress in school. In Kindergarten, it’s CCSS.Math.Content.K.OA.A.1. In first grade, it remains the same standard and extends to CCSS.Math.Content.1.OA.C.6. In second grade, these two standards continue to grow as well as CCSS.Math.Content.2.OA.B.2. By the time students reach third grade, addition and subtraction should be mastered so that students can start to conceptually understand multiplication and division. Additionally (no pun intended), it can help guide second grade students in developing CCSS.Math.Content.2.NBT.B.5 which deals with base ten operations (although this standard goes to 100 and the app only has students adding to 20).
Cognitively Guided Instruction
It’s only been in the past few years as I’ve been introduced to Cognitively Guided Instruction (CGI) that I’ve really been able to see numbers in a new way. I wish, I wish, I wish I could have learned mathematics in this way as a child, and I wish this for my own children. Younger elementary students don’t need worksheets— they need to use their intuition and workable objects, and they need to conceptualize the properties of mathematics so that they can apply those properties as they get older and start learning how to do more complex problems. Truly, the best way I’ve seen for teachers to help students meet the Common Core State Standards and to fully develop their skills in Mathematics is to become educated in CGI.
What Do You Think?
What experience do you have with the conceptual understanding of mathematics? Do you think that students should have a strong conceptual understanding before moving on to the standard algorithm? Do you know of any other apps (besides ST Math/JiJi) that might support this?