This will begin a series about our new math program. I have included a great article at the end of this blog, written by Solomon Friedberg, the chair of the math department at Boston College.
Kindergarten Math/Reading – Mrs. Gore had her Kindergarten students guess the number of seeds in a pumpkin, and then write the number. They had read books about pumpkins, and counted pumpkins as they read. This is a good example of integrating math in another subject.
Math games are always fun!
When students know what the learning goal is for a lesson, it helps reduce stress around new learning, and keeps everyone focused.
Our new math program asks students to really think about math, rather than just memorize facts. Memorizing facts is still important in order to be able to do the math within the complex problems. You may have noticed that math homework is taking more time because of all of the complex problems, and the explanations. As students get used to doing these problems, they will be faster. Math in the real world is generally more complex than a simple computation. We usually have to think about what kind of math we need to solve real world problems. If I want to tile my kitchen counter, I have to know more than the formula for area. I have to know how big each tile is, and how many I will need for the surface area I am covering. Knowing basic multiplication is very helpful, but only after I figure out what I need to multiply. Underlining the actual question in a word problem, and then looking for the important information in the problem, are essential skills to solving complex math problems.
How have you used math in the past week? Was it just a computation? Did you simply use an algorithm, or did you need to do more than one step to find your answer? As you see yourself doing math in your day-to-day life, point that out to your children so that they see the value of problem solving and fact memorization.
Common Core math is not fuzzy: Column
Solomon Friedberg7:43 p.m. EDT September 15, 2014
Real fluency is an improvement on traditional math’s plug-and-chug, mechanical approach.
Common Core math is getting the works from critics: It’s too demanding for most kids; holds back the speedy kids; not the same as what parents already know; makes kids cry. It even promotes “fuzzy math.”
As a professional mathematician, I’m as firmly against fuzzy math as they come. Common Core lays the foundation for students to have a better grasp of mathematical concepts than present standards and sets higher expectations for teaching and learning.
If that doesn’t sound fuzzy, there’s a simple reason: It isn’t.
To appreciate the changes under way, and perhaps to understand the anxiety provoked by Common Core, it’s helpful to look at math before the core.
Too often, it has been “plug and chug” math. In this approach, math is a bunch ofmemorized rules that don’t make much sense. Follow the rules, and you will get the right answer. Do something different, and you’re likely to get it wrong. “Analyticalthinking” consists of figuring out which rule to apply. There is limited need for originality, explanations, or even genuine understanding. Learning enough rules will allow you to solve the problems you are given. Do this for enough years, and you may firmly believe that this is what mathematics actually is. If your kids are asked to do something different, you may be up in arms.
Reality of rules
Math as rules starts early. Kids learn in elementary school that you can “add a zero to multiply by ten.” And it’s true, 237 x 10 = 2370. Never mind why. But then when kids learn decimals, the rule fails: 2.37 x 10 is not 2.370. One approach is to simply add another rule. But that’s not the best way.
Common Core saves us from plug-and-chug. In fact, math is based on a collection of ideas that do make sense. The rules come from the ideas. Common Core asks students to learn math this way, with both computational fluency and understanding of the ideas.
Learning math this way leads to deeper understanding, obviates the need for endlessrule-memorizing and provides the intellectual flexibility to apply math in new situations, ones for which the rules need to be adapted. (It’s also a lot more fun.) Combiningcomputational fluency with understanding makes for problem solvers who can genuinely use their math. This is what businesses want and what is necessary to use math in a quantitative discipline.
Here is what good math learning produces: Students who can compute correctly and wisely, choosing the best way to do a given computation; students who can explain what they are doing when they solve a problem or use math to analyze a situation; and students who have the flexibility and understanding to find the best approach to a new problem.
Common Core promotes this. It systematically and coherently specifies the topics and connections needed for math to make sense, and promotes both understanding and accuracy.
This doesn’t sound revolutionary because it’s not. Common Core is a list of topicseveryone knows we should teach. It doesn’t tell teachers how to teach them (though it does ask that they teach them coherently, with understanding). It is also not a test, not a curriculum, not a set of homework problems, not a federal mandate and not a teacher evaluation tool.
But you wouldn’t know it from some of the criticisms directed at it. It lays out the topics for students, grade by grade. The rest is up to the teachers, school districts and state boards.
The higher expectations laid out by the Core have been endorsed by every major mathematical society president, including the American Mathematical Society and theAmerican Statistical Association. They called the Common Core State Standards an “auspicious advance in mathematics education.”
Of course, the core will do best if parents can support their children in reaching these higher goals. Websites such as Khan Academy and Illustrative Mathematics have incorporated the standards and show best practices and well-crafted math problems.
There is no doubt that the new standards are more rigorous. They will require more of our students, our teachers and our parents. Knowing what you are doing, instead of just knowing a set of rules, is the essential foundation for applying math to the real world.
That’s not fuzzy. It is smart.
Solomon Friedberg is chair of the Math Department at Boston College and an editor of the book series Issues in Mathematics Education.