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Mathematics

 

Overview

Brookwood has recently adopted a K-5 math program, Investigations in Number, Data and Space.  We find that this program is an excellent fit for our goals and mission as a school.  Using this program means that we are working with the most current information about what math children should learn at each grade level, and about how children learn math best.

This program differs in a number of ways from the traditional math programs most adults had as elementary school students.  How is Investigations different from other math programs?  What should you as a parent expect?  The answers are hard to summarize, but here is a quick orientation.

Concept development:  In Investigations, students start a new topic with a problem-solving experience.  They then construct an understanding of the math through discussion that is carefully guided by the teacher.  (This, incidentally, is the model for math lessons used in Japan, which is consistently one of the highest-scoring nations in math in international testing.)  The goal of these activities and discussions is to help students develop a deep level of understanding of important mathematical concepts.  Also, the problem-solving activities are designed to allow students to use multiple approaches.  They can use visual and hands--on models-not just words and symbols--to solve the problems and to show their thinking to someone else.

Fact practice:  Much of your child’s math fact practice will happen through games.  This approach allows children to have lots of practice in a way that is more motivating to them than simple pages of drill problems, although we will use those from time to time as well.  Keep an eye out for information about the math games.  Finding time to play the games with your child at home is a great way that you can support his or her math learning.  Teachers periodically assess, one-on-one, students’ level of mastery of math facts.  Games, activities, and assessments follow a carefully chosen sequence of “families” of facts such that students master one group at a time, and eventually know all the basic combinations from the “plus 1” addition combinations through the 12 x 12 multiplication combinations and related division facts.

Addition, subtraction, multiplication, and division:  Most of us learned one way to do each of these operations, methods known as “traditional algorithm”, often without understanding how they worked or why they made sense.  Interestingly, most of us don’t use those algorithms for all the “real life” math that we do—we often use “tricks” and shortcuts that are really algebra in action, and that allow us to do math more quickly.  Investigations encourages students to use multiple strategies in addition to the traditional algorithms.  This strengthens their powers of calculation because it helps them not only how to get an answer, but why that answer makes sense.  Furthermore, this approach develops the crucial mathematical skill of doing a problem more than one way to confirm that the first result is correct.  It is likely that your child will use language and procedures that are unfamiliar to you for these operations, while your language and procedures might seem to surprise him or her.  When this happens, do your best to explain to each other, realizing that at any given time, your child may not be ready to understand your way…and vice versa!  Sometimes learning to do a math procedure in a different way is like learning to speak a foreign language; it can be hard to understand one when you are still “thinking” the other.  Give it time, and know that our goal, like yours is for your child to become fluent in mathematics.

Emphasis on thinking, understanding and explaining:  For most of us, elementary school math was about learning procedures, and success was only about doing a lot of problems quickly.  Many students who succeeded with calculations struggled later on with courses like algebra and geometry because they had skipped the building blocks for abstract reasoning, proof, geometric visualization.  We now know that elementary school children can and should focus on those building blocks, as they do in many other countries.  Children should consider why 27 + 58 is the same as 30 + 55 (you might not see it, but this involves algebra), and they should be asked to explain how they know a math statement is true (this is the basis of writing formal proofs). 

Scope and sequence:  Because Investigations emphasizes depth of understanding, and because it draws attention to algebraic and geometric reasoning early, your child will cover math topics in different grades than you might remember from your own school days.  Some topics might seem surprisingly early, and others surprisingly late to you.  For example, the multiplication facts up to 12 x12 are taught, but complete mastery by all students is not expected until the fourth grade.  Be aware that as a whole, our use of this program will ready students to enter sixth grade math where they need to be.  Our colleagues at other Investigations schools tell us that as their students enter sixth grade, they not only have mastery of the content they need, but they also have sophisticated problem-solving skills, an ability to think deeply about math concepts and to communicate what they know, and an appreciation of math as an enjoyable, worthwhile pursuit.