Good afternoon and welcome to NCTM President Cathy Seeley’s online chat. The topic today is her President’s Message on “Seek First to Understand.” Our first question is from
I saw a table recently showing that other countries spend more time on just number sense/computation in the primary grades, and judging from the U.S.’s much lower scores that seems to be a better option. I wonder if, in trying to teach all the strands, we never allow students to become proficient at any one of them. Should we be changing our emphasis and concentrate on just 1-3 strands in primary grades, make sure students are fluent with those, and then introduce others?
I don’t think it’s so much a matter of eliminating some of the strands, but rather of prioritizing them. Much of the work at the early grades with data, measurement and geometry, for example, can be used to support the development of an understanding of numbers and operations and can also provide contexts for solving problems. The current math curriculum in most states consists of a list of unprioritized standards or expectations that frequently includes 50, 60, 80 or more statements for teachers to address and/or for students to learn. Clearly, there needs to be a way to focus our attention on priorities and connect these many pieces into a coherent instructional program, as called for in NCTM’s Principles and Standards for School Mathematics. NCTM continues to explore ways to provide this kind of support.
To overcome barriers, we must get out and learn the communities. We must form math clubs, chess clubs, etc. and enter competitions that will expose us as well as our students to other communities, cultures, and learning environments.
Reaching out to the community can be an important and relevant way to shape what happens in the math classroom and to give teachers a broader perspective of their students’ lives. Thanks for sharing this idea.
St. Charles, Missouri
What strategies are American mathematicians employing to change our measurement system to metric?
The American public is constantly bombarded with how poorly American students do on international math assessments compared to other nations. Yet no one defends the amount of instructional time spent in teaching fractions rather then higher level or other concepts more in depth.
Is it also possible that part of our “competitive edge” has been dulled in international trade because we lag so far behind the rest of the world in measuring units?
When I started teaching math 35 years ago, I told my junior high students that by the time they would be adults, this country would surely have gone to exclusively using the metric system. Apparently, I was wrong. I fully concur that we need to join the rest of the world in adopting this logical decimal system of measurement. Realistically, however, our students in this country appear to face a future with two measurement systems.
Meanwhile, I think our problems with fractions run deeper than measurement. Measurement can provide a meaningful context for fractions. But we need to do a much better job of teaching fractions well. Right now we often skim through the conceptual notions of fractions and race to the rules, often without meaning. Then when students haven’t learned the rules the first time through (sometimes as early as grade 4), we have to un-teach and re-teach year after year. I’d like to see us learn a lesson from other countries here and postpone the teaching of fraction rules until students have a solid understanding of what fractions are (in terms of both parts of a whole and parts of a set) and how to compare fractions. Then we can invest in teaching fraction operations with meaning and for lasting learning that can serve students well into both everyday problems and advanced mathematics courses.
Wilson, North Carolina
Our high school math classes work with the engineering department at the local university. Students get to tour the classrooms and ask professors and college students questions. It's a great way to show the application of the mathematics they are learning today.
This is a nice example of a collaborative working arrangement between a high school and a university. This is not the first time I have heard of an effort in North Carolina to support math, science, and engineering programs at both the high school and post-secondary level. Thanks for building these bridges and for sharing this good example!
I am considered not to be qualified to teach Math because our district and middle schools are requiring Multiple Subject Credentials for Single Subject Requirements for Single Subject teaching. Although “highly qualified” to teach Math I lack two K-2 Reading courses (which I would not have been required to take 5 years ago).
I have 70 equivalent semester math credits, have passed the CSET and have served in a math leadership position--NCTM/GSDMC--VP, Pres. Elect, Pres. for the past seven years. You see, even though I have a second major from the U.S. Naval Postgraduate School in Operations Research the district won’t honor it because it does not say “Math” (though the course included the text “Advanced Engineering Mathematics” by Erwin Kreyszig).
We are all screaming for math teachers and I am frustrated.
I don’t blame you for being frustrated. It sounds like there needs to be a way to tap into the resources of a person with a strong math background. Sometimes such programs come from the district, sometimes from the state, and sometimes from a university. It sounds like you are connected to a range of professional activities. Perhaps your local math group can work with the district to encourage or develop a program for non-routine routes for certification. As we expand these alternative routes, however, we have to be sensitive to the demands on teachers and recognize that sometimes people coming from other fields may need support, just as new teachers from more traditional routes. Teacher quality is a complex issue, and I fear we have not yet solved many of the problems surrounding it.
Toms River, New Jersey
What kind of profitable dialogue can we have with different groups with regards to technology? It seems as though many parents, who use calculators regularly still feel uneasy about the role of calculators in school.
This issue is one that begs for constructive dialogue across communities. Often I find that those who are outside the classroom, or even educators who may not use technology, may fear that allowing calculators might undermine a student’s mathematical learning. I find numerous examples to the contrary, however. A teacher who uses calculators well will modify the kinds of problems he or she gives students, tapping into the capabilities of the calculator to allow students to work on higher level and on more complex mathematics than they would otherwise be able to do. The teacher will also identify when it is not appropriate to use a calculator, so that we prevent students from becoming dependent on these powerful tools for simple math that students should be able to do in their heads, such as multiplication facts or dealing with powers of ten. I have found that the most successful schools in this arena have reached out across the various communities they serve to invite people into successful classrooms that have integrated the use of this tool. This might happen during the day or in evening or weekend “Family Math” events. When someone sees students thinking and reasoning while using a calculator, they are usually convinced of the potential.
Audubon, New Jersey
It seems that parents just want their children to learn the standard ways of doing arithmetic. They are not so much interested that the students understand what they are doing. What can I say about all the extra time I’m spending trying to get students to understand what they are doing?
This is a common concern that lies at the heart of the problems with the American math program. In recent collaborative discussions with mathematicians, I think it’s fair to say that both mathematicians and educators agree that we need to teach students both how to do math and how to make sense of what they are doing. It comes back to building understanding, proficiency, and the ability to solve a range of problems. Teaching well for understanding can prevent a lot of re-teaching later.
I was looking for old tests on the MATHCOUNTS coaches Web site and found a new coach who I offered to help. He turned out to be an actuary and has taught both me and my students better ways of solving problems. Students feel comfortable e-mailing him or me—he’s like a co-teacher. He uses combinatorics to solve problems much more frequently than I used to. I’ve also used parents and friends who have expertise in math. Biggest barrier is time to organize.
This is a great story. Time continues to be a huge variable in teachers’ ability to teach the way they know will help students learn. Thanks for sharing these good ideas and this serendipitous collaboration.
I enjoyed reading your article, “Seek First to Understand.” With understanding comes self-awareness of our own limitations. It takes effort on everyone’s part to learn to really listen to each other. We all seem too busy and preoccupied in our own thoughts. Thank you for sharing. I agree with what you said in your article. I need to ponder further to truly understand. Aloha.
Thanks for your comments. I think we could all benefit by pondering further and reaching out on our path toward understanding.
Thank you for your participation in today’s chat, which will be Cathy Seeley’s last as NCTM President. We appreciate your interest and engagement in these exchanges.
I want to thank all of the participants in all of our eighteen chats. These chats have been a great opportunity for me to expand my understanding of the issues you all face, not to mention an opportunity to think on my feet! Whether we receive a question in advance or during the chat, it always stimulates my thinking. I’ll look forward to other opportunities and other vehicles for interacting with all of you over the next few years.
"Seek First to Understand " (April 2006)
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