After focusing recently on changes we are making in elementary math instruction for students and teachers, I would like to talk about the middle school math Program. Parents often find the lack of examples in the Connected Mathematics books confusing and frustrating. Why are examples not available and what have we done to make parents’ lives easier at homework time?
Before reform efforts began in mathematics instruction in the early 1980s, a nationwide assessment asked students to estimate the answer to the following problem: 12/13 + 7/8. The multiple choices given were 1, 2, 19 and 21.
Most 13-year-olds and 17-year-olds chose 19 or 21 instead of the correct answer of 2. Why? Rather than realizing that each fraction was almost one whole, and 1+1 = 2, they tried to use the rules they had memorized about fractions, making mistakes or becoming confused by the many other rules crowding their minds.
When children learn by memorization without understanding why the steps work, they tend to confuse and misapply rules later on. This is one reason many students seem to do well in math during elementary school, only to become frustrated and confused in middle school.
I witnessed it many times in my 10 years teaching at Kodiak Middle School. Students had many procedures memorized, but when they reached my classroom, they had to decide when to use which steps. I heard these and other similar questions many times: “Do we divide or multiply to solve this one?” or “What number goes on the inside of the division sign?”
Even more distressing is the child who adamantly insists, “You CANNOT do 5/7! It is impossible, you have to put the big number on top.”
This belief makes teaching addition and subtraction of positive and negative numbers agonizingly difficult.
This is why there are no examples in the book. We want students to make sense of the mathematics, notice patterns, and formulate methods for solving the problems.
One of the most rewarding moments in my teaching career was when a student announced that they had “discovered” the reason behind the Pythagorean Theorem, or “invented” a formula for finding the area of a circle.
So what is a parent to do without access to the teacher’s guide and knowledge, built after years of experience? There are several resources available. The CMP (Connected Mathematics Program) website http://connectedmath.msu.edu/, while reported by some to be difficult to navigate, is a source of much information.
A more user-friendly resource can be found on the KIBSD Website (www.kibsd.org) under “Families & Parent Resources” or use the following link: http://www.kibsd.org/subsite/dist/page/parent-resources-7123.
In this online resource you will find, in addition to career tech and reading resources, an extensive list of downloadable math resources from first through eighth grades. Each two-page download provides you with a description of the content of the unit followed by a table with specific examples of how each piece of the content is taught.
Additionally, I have found another school district’s website which has a many valuable tips, homework help advice, and gives guidance on almost every single investigation and homework problem in the entire Middle School Connected Mathematics Series: http://www.smfcsd.org/math/athomeCM2.htm.
I am always interested in feedback regarding the KIBSD math curriculum. If you have questions, need more information, or have suggestions, please feel free to contact me anytime.
Christy Lyle is the math coordinator for the Kodiak Island Borough School District. Contact her at 481-6527 or email@example.com.