Solving for X in Primary Grades

Oregon's Lebanon Community Schools District is pushing algebra content as early as 1st grade, and the approach is yielding positive results.

Elementary math classes in Lebanon don't rely on memorization, flash cards, or worksheets. Instead, students are encouraged to write their own equations, discuss their mathematical reasoning at length, and work with hands-on models of math concepts.

Lebanon's approach to math instruction is based largely on a teacher training technique called cognitive guided instruction (CGI). Developed by researchers at the University of Wisconsin at Madison, CGI supposes students know more about math than assumed, and by asking students to talk about their reasoning, teachers can guide students to deeper math knowledge.

Researchers at Johns Hopkins recently found that "getting teachers to change their daily teaching practices does more to raise math achievement than buying new textbooks or computerized math programs" (Oregonian).

Comments

[kddidit]

It is SO refreshing to read about primary level teachers who willingly play with math. I spent 11 of my 36 years of teaching in primary grades and worked with good teachers who knew literacy BUT did not know math. I marvel that as many students do learn as much math as they do given the lack of exposure to number theory, problem solving and solving using an unknown in the primary grades. I found it very easy to catch fourth graders up on math because I knew what they hadn't been taught in their prior years.

NOW, if we could convince someone to develop a full-fledged hands-on geometry for primary teachers so there wouldn't be a need for remediation in 10th grade. But that is another story!

[Shirley Milne]

To think that our problem in Melbourne (Australia) occurs in USA! We really need to work together to solve this - perhaps this "Across the Pacific" communication is one way to start.

[Wally]

The PROBLEM is that there are very few, if any, Math Specialists in the elementary/primary grades. As noted above and was confirmed in the report by the US National Panel on Mathematics the elementary school teachers are Generalists whereas they should be Specialists.
As a high school teacher of mathematics I have interacted with many elementary and middle school teachers and although they are all very nice people and stive to do their best they simply do NOT, as Li Ping Ma puts it, have a deep and profound understanding of number let alone mathematics (I'm not indicting all of them, of course there are exceptions but this is true as a general rule.) Ask any elementary school teacher why they chose that level and the majority of them will tell you because they love the kids. Dig a little deeper and the obvious surfaces = they were never good at math in high school and math in elementary school is well = elementary. This is where the problem lies. For additional evidence of math ineptness of teachers in the lower grades just look at the PRAXIS data and the extraordinary measures that Schools of Education take to get their students to pass the Math portion of PRAXIS I; a test which requires no knowledge of math concepts above 7th grade, hmmmm??? Why do so many do so poorly? They know the algorithms BUT they do NOT understand the concepts! Just ask youngsters what is 20-7 is and see how many cannot give an answer without writing te numbers down on paper and then going through the regrouping algorithm. So when these students eventually pass and become certified are they highly qualified to teach mathematics? Of course not. How do they teach the required mathematics? They teach what they know = the algorithms which is the LOWEST level of teaching and learning and has nothing to do with conceptual learning and developing understanding.
To solve this problem requires elementary students to be taught by a Math Specialist who HAS a deep and profound understanding of number AND mathematics. The physical arrangement in the elementary school can be the same BUT when it is Math Time the Math Specialist comes in with her/his cart with all of the maniplatives and tools of the trade for the lesson. The certified elementary school teacher assists.
There will always be isolated pockets of excellence but nothing will change overall unless there is a concerted massive push at ALL levels to develop Math Specialists. This doesn't mean that this person should be a math major. What it does mean is that special training is needed for potential teachers of mathematics at the elementary school level can develop the deep and profound understanding of number and mathematics so that they in turn can translate that into CGI in the elementary schools.

[Jennifer]

As a graduate of the University of Wisconsin-Madison, a high school mathematics teacher, and the parent of a kindergartener, I feel compelled to comment on this post for several reasons. First, it is great to hear of the success of a program developed at UW. Throughout my undergraduate training in mathematics education, we were consistently taught that students are capable of very sophisticated mathematical thinking and reasoning at a rather young age...if we only gave them a chance to do so rather than drill and kill them with algorithms. I see this in my own daughter, who, in kindergarten, can identify shapes my 10th grade geometry students couldn't, and understands more about patterns and symmetry than most adults. I think mathematics teachers, whether they are specialists or generalists, need to find a happy medium between teaching reasoning and problem solving skills and basic facts. Too often, we see students at the high school level who are lacking basic arithmetic skills because proficiency in basic facts was not emphasized in the primary grades. Calculators are a great tool, and can help many students who struggle with basic computation move on to higher levels of mathematics, but it always makes me cringe when a student would grab their calculator for something as easy 3 + 10, or worse yet 8 x 0.

One final note. For those of you looking for a resource for your more literacy minded elementary colleagues, I highly recommend "Comprehending Math" by Arthur Hyde, who explains how to incorporate reading strategies into the teaching of mathematics K-6 (it's good for secondary teachers too).

[Lillian]

Right on Shirley! I taught elementary Math only for 3rd and 4th graders and they are excelling in middle school. We are leaving kids behind and it is difficult for a middle school let alone high school teacher to fill in that many gaps. I speak from experience, I have taught 3rd, 4th, 6th, 7th and 9 grade math, as well as GED. I was also Curriculum Specialist for an Upward Bound Program. In Texas, about 40% of the test to graduate is middle school math. Standards are low because effective teaching is not occurring in the early years.