I grew up in a household where mathematics was held in high regard. My father was a road construction superintendent with a high school diploma. He challenged us with real-world math problems at the dinner table on weekends when he was home.
While I had limited involvement with my three older stepchildren's math education, I have always tried to promote a positive view of math and science in our household. One of our older boys graduated with a degree in manufacturing engineering and the other will graduate this year with a bachelor's degree in biology. I began to develop a real awareness of elementary school mathematics when I started volunteering at my daughter's grade school eight years ago. When our oldest daughter was in primary school, volunteering meant reading with students. As a former Stanford-educated civil engineer, I didn't know much about how children learn to read. I often left the school wondering why teachers never asked me for help with math and when I would see my kids do something different from what I experienced in my elementary math education.
By second grade, my daughter's teacher was giving students timed tests on their math facts every Wednesday. My observation was that a few students were successful week to week, but at considerable expense to everyone's psyches and self-esteem. My daughter cried every Wednesday morning before she went to school. During that school year and the next, several things happened that changed my view of elementary and middle school mathematics forever. The first was a telephone call I made to my older sister who has taught college algebra and reformed calculus for 12 years. When I asked whether I should expect my children's math education to look so similar to what she and I experienced in the 1950's and 60's, she suggested I get on the Internet and search for the word "numeracy." The next thing was my attendance at a public meeting entitled, "Your Child s Mathematics Education: What You Need to Know" given by Ruth Parker from the Mathematics Education Collaborative in Bellingham, WA. The audience had opportunities to do some mental math, to think about the value and possible shortcomings of traditional mathematics education, and to wonder about what our children will need to be able to understand that we never even needed. A final thing happened within that same year. Portland Public School officials proposed to the school board that the District implement standards-based curricula at both elementary and middle school, after 11 years of allowing teachers to use whatever mathematics materials they believed were valuable.
I had become more familiar, after the Ruth Parker talk, with NSF-funded materials and knew teachers who had been teaching the Investigations curriculum for several years. Portland proposed adopting Investigations and Connected Math. I was delighted and prepared testimony for the school board in support of the reformed choices. Testimony was that I was someone who had always appeared to be successful learning mathematics, but was actually just good at doing what I was shown. Even though I took the required mathematics courses I needed to take to earn my Bachelors degree in Civil Engineering from Stanford University, I had a rather shallow understanding of much of the mathematics I studied. So I was very excited by the prospect that my daughters might learn mathematics in a more meaningful way. I was excited about this change for my own children, who I knew would get good support for their math learning at home. But, I felt the most hopeful for the many students around the district who would have had to rely only on what the school had to offer without that kind of enrichment.
What I'm seeing in my daughters, now in seventh, sixth and first grades, are demonstrations that mathematics is meaningful and a level of understanding that I didn't have until I was much older. They rely on models to show their understandings and they strikingly never come to me with a request like: "Can you show me how to do this?"
Their questions instead are: "If I show you how I think this works, will you let me know if I am on the right track?" "Can I show you how I'm thinking about this problem?" "Does this make sense so far?" "Will you work this problem while I'm working it then compare answers so I can see if I'm thinking about this correctly?" "Is this a good way to represent this idea?" "Could I use the same model with this problem as I did the others?" I am impressed and grateful for the education they have received. It is not the same early education my high school students received and their experiences with and feelings about mathematics are far different from my children.
Students in my advanced algebra course, mostly juniors and seniors, are too old to have been introduced to Connected Math in middle school and are oriented to being shown how to do math in a procedural way. My freshman students have had some experiences with a standards-based curriculum, but it was during the transitional period when the teachers were getting familiar with new instructional methods. What I look forward to, is the day when freshmen come to my class with six years of Investigations and three years of Connected Math behind them. They will be accustomed to using models and exploring math concepts in depth and comfortable with communicating their understandings in a variety of different ways. I look forward to them coming in with the confidence and attitudes that my daughters have toward math, because they know deep down that they can figure things out.
Because I grew up in a household where studying math, science and engineering was supported, I have had many opportunities to work, travel and participate in the world. I also have an MBA from a top tier institution that has provided access to further educational and career opportunities. To a very large degree, I have been able to do what I wanted because I was raised with the belief that I can do math and that to do math is a good thing. It is an irony that we live in a math-phobic culture that excuses a person who can't compute the tip on a restaurant bill, yet we pave the road for people who demonstrate proficiency in mathematics.
Susan Pfohman, Engineer, Parent, and High School Mathematics Teacher
January 2003
This information was reprinted with permission of CESAME, Northeastern Univ., and the Educational Alliance, Brown University.
