Algebra from the Primary Perspective

Okay? You want me to comment on Algebra?, was my first reaction to our assignment. Before I muddle forward with any discussion regarding the subject of Algebra let me layout some background information. My "eighth grade experience" with Algebra was in the 10th grade and it was 40 years ago. Having taught either preschool or primary grades, mostly kindergarten, in the last 30 years, my contemplation of Algebra has been limited to thinking about my own children and their various experiences with Algebra. Out of 4 of our children the youngest who is now 24 took Algebra in the 8th grade. A comment he once made during his eighth grade year has stuck with me and echoes in my mind whenever I work with students and the idea of equations. My son said,
"Teachers should really use blocks to help kids understand Algebra." Incidentally, my son enjoyed math a great deal, tried it as a major in college, and finally settled in the geosciences.

Blocks! What do they have to do with the article "Recalculating The 8th Grade Algebra Rush? Before I contemplate that question I want to focus on a small quote from the article that struck me as the heart of article and is also very connected to my thinking about blocks. The last paragraph states,
"It would be better to think of Algebra as we do swimming: something everyone should learn, most importantly learn well. Get everyone into the pool as soon as possible. But let's not mark them as having passed the course until we are sure they can swim several lengths without drowning"
I am also a swimmer and past teacher of swimming. Of swimming I can say: not everyone learns swimming at the same rate, over the same length of time, through the same methods of teaching, or with the same amount of practice. H-m-m-m, that sounds familiar; Teaching Methods 101, differentiating instruction.

This quote illustrates a developmental perspective in that any given skill, in this case swimming or Algebra, each need time to develop, have an individual component for each learner, and in the case of either, to be useful to the learner they have to be firmly connected to prior knowledge (learned well). From the perspective of a primary level teacher where student thinking is very concrete and connected to real objects that may eventually be represented by equations, blocks and other math manipulatives become an integral mode of teaching. Blocks are a concrete medium through which students can develop theories, test their thinking and make conclusions. Unit Blocks, the large, blonde colored blocks that need their own shelf in most kindergarten rooms, can be used to build equations: block size A = 2 of block size B or A = 2B. Similarly, Cuisinare Rods also give rise to exploring equivalent relationships. From my experience, concrete exploration with materials that can be manipulated and assist in evolving mathematical thinking is a key developmental component that lays ground work for Algebraic understanding. The reason why my son's comment has stuck with me is that it illustrates how the cultivation of well-based new learning has a connection to prior knowledge and experience. In his case to all the years he played with blocks and legos. Starting with block and other manipulatives, a concrete model to bridge mathematical knowledge to the abstract world of Algebra can be built.

So what do all my ramblings have to do with "the 8th grade rush?" I believe learning is developmental and experiential, not everyone will be ready in the 8th grade for Algebra. Whether any given student is developmentally ready for abstract thinking (Piaget- formal operations) and to learn Algebra will vary from individual to individual. Experientially I wonder what role the primary teacher plays in providing concrete investigative experiences on which bridges can later be built for learning Algebra and learning it well. Thinking of "getting everyone into the pool as soon as possible, what do you think our role, if any, as primary teachers is regarding the development of mathematical thinking that leads to learning Algebra well whether it be in the 8th grade or later?