The state of math today
Our curriculum is always evolving.
From the ever-changing state assessments to the increasing rigor of the new Common Core standards, the educational landscape of today is transforming so quickly as to be unrecognizable. As confusing as it may be to educators, it is even more so to parents and students.
But it doesn’t have to be this way. At Swun Math, we work with both educators and parents to deliver the best math instruction possible to our students. On this site, we will provide lots of simple, useful tips for math teachers, math students, and parents. All these tips can be used right away, though consistent practice will make them even more effective.
For us, it’s personal
Our founder, Si Swun, was an immigrant to this country. As a student and English language learner, he struggled with math, an experience that would later shape his perspectives on education–and inspire him to go into education. As a fifth-grade math teacher at Long Beach Unified School District, Si’s students were incredibly successful on state assessments–so much so that LBUSD asked him to create a pilot program for some of its lowest schools. At one of the pilot elementary schools, one year later, the percentage of students rated “proficient” doubled from 22% to 45%; six years later, the number tripled to 66%.
Afterwards, Si founded Swun Math to bring his vision of mathematical mastery to schools, districts, and regions across the country.
Learning starts at home: advice for parents
The biggest factor in student success is home support. The good news is that elementary math is very concrete and straightforward, with plenty of visual aids, such as charts, tables, or number lines, to help in the solving process.
Of all these visual guides, perhaps the important one is the multiplication table. Certainly most parents memorized multiplication tables when they were in grade school, and today, the times tables are still a very useful tool because it offers a quick, easy shortcut for solving problems–especially if you don’t have a calculator.
However, parents have to understand one thing: Common Core fundamentally changes the way that numbers are taught to students, giving a framework that is totally different than what parents might be used to. Also important is the fact that students must show how they arrive at an answer.
For instance, let’s take a look at this viral example, where a student was marked wrong for writing that 5×3=15, because (s)he had worked out that 5+5+5=15. Both calculations (5+5+5 and 3+3+3+3+3) arrive at the same answer, due to the commutative property. But there was still an issue: as the article points out, 5 x 3 should be read as five groups of three, and not three groups of five.
Think of it as packaging. You can sell five A packages (each of which contain three phone cases), or three B packages (each of which contain five phone cases). But while the total number of phone cases is the same (15), there’s definitely a different price for package A (with 3 cases), as opposed to package B (with 5 cases). It’s this distinction that Common Core wants to point out.
Another one would be the use of ten frames, which are two rows of boxes, with five boxes in each row (totaling ten boxes); each box is either filled with a dot to indicate a value, or left blank, to indicate a zero. Ten frames are very easy to use, simply because they allow students to quickly count; for instance, leave out three boxes on a ten frame, and students can quickly see that it is seven.
The reasoning behind ten frames is that, like counting in groups of five, ten frames offer an easy progression for students to quickly understand number theory. After all, subtracting from ten frames is much easier than counting the individual numbers, one by one. And, it allows children to construct other ways to recognize values. For example, 7 is 2 more than 5 (a full row), and 3 is less than 10.
And making a simple ten frame at home is also quite easy: just take an old egg carton and cut off the last two ends for your own ten frame. This way, you can supplement your student’s learning at school with manipulatives (we call these objects manipulatives because they can be physically handled) of your own.
Going into the classroom: advice for teachers
Manipulatives are also standard equipment for teachers, who rely on these physical objects to teach students abstract reasoning skills. For the best effect, use manipulatives that come in a variety of colors, sizes, and shapes. For example, you could use a round, spherical object, like an orange or a watermelon, to show volume, or a flat, two-dimensional thing, such as a pizza, to show fractions.
Some great additions to your wall
An interactive number line is also very helpful, given Common Core’s emphasis on multiple tools and strategies as pathways for students. A simple number line, made from construction paper, with a movable arrow, can really help your students see the relation between negative numbers and positive numbers.
Also very helpful is a large, oversized protractor, which would make a nice addition to any empty bulletin boards. While protractors are indispensable in teaching students about the measure of angles, they are also quite small, with tiny, hard to read numbers denoting the degrees. With that in mind, an oversized protractor posted on your bulletin board, with two paper arms–much like a giant, half-clock, could go a long way to helping students understand the mechanics and principles behind measuring angles.
Note that both of these tools can be scaled down to individual sizes, if needed. For instance, you can make a template of a simple number line on Word or Powerpoint, print it out, photocopy, and distribute to students.