eNumeracy

Today, I thought of a quote from Thoreau's Walden. In his discussion of economics (essentially - resource allocation in society), he writes,

"There are a thousand hacking at the branches of evil to one who is striking at the root, and it may be that he who bestows the largest amount of time and money on the needy is doing the most by his mode of life to produce that misery which he strives in vain to relieve."

In my experience trying to focus on early intervention and prevention in grades K-2, there is a general belief that, because things are not obviously problematic, we don't necessarily need to change. Although normative differences are indeed noticeable in K-2 settings, they rarely produce such a disruption to the overall environment to warrant large-scale targeting. Teachers work harder in the classroom, reducing down numbers of students at-risk, but schools may not be providing the types of support to alter the status quo and prevent problems by solving them. Intensive number-focused intervention shows significant promise (see blog post featuring data presented at NASP), and the North Carolina State Improvement Project has the numbers to support this as well.

The National Mathematics Advisory Panel (NMAP), in 2008, placed a heavy emphasis on teaching and learning algebra. My fear is that due to this emphasis, all types of resources may be re-allocated to the upper grades where algebraic thinking first begins to develop. While I was doing a talk at the RtI Innovations conference in Salt Lake City in 2008, I was confronted by the Chief Academic Officer of the Los Angeles United School District. She indicated that the focus on early numeracy is interesting, but her charge is to improve middle and high school education, as a direct result of their district's planning after the release of the NMAP. She was hoping to glean new and innovative knowledge to help her achieve her goals. After this healthy confrontation, I asked her why someone of her influence does not try to solve these problems by allocating resources to early intervention and prevention. She replied that her hands were tied: resources go to the upper grades. After thinking this through, I thought that maybe this is because the field lacks a consensus on exactly what concepts need to be taught in the early grades, and which concepts predict success in algebra. I also thought that this tendency is ingrained, human, and perhaps societal: throw money and resources at problems that we can see.

While it is important to allocate resources to those who need it, what are the roots of algebra that develop in pre-kindergarten, kindergarten, and the primary grades that, if mastered, lead to a strong development of math skill? Schools are notorious for responding to problems after they become evident and after they have an impact on a larger scale. Unfortunately, a child in third grade two levels behind will cause a stronger impact than a child in kindergarten who cannot count to twenty, compare relative size, and order numbers. Why? The gaps are smaller.

If I sound like a broken record, or someone walking around with a hammer looking for nails, I don't mind: the only way to solve problems are to prevent them from occurring in the first place. Primary prevention and early intervention in schools and at home is where we need to allocate our resources.