There is hope – at least in some quarters – that the Common Core State Standards (CCSS) will bring an improvement in math education. According to the CCSS website, the new standards “[i]nclude rigorous content and application of knowledge through high-order skills” and “[a]re informed by other top performing countries, so that all students are prepared to succeed in our global economy and society”. It sounds exciting and indeed, when one reads the standards, one does see an attempt to connect concepts and to ask students to think rather than memorize a set of unrelated facts.
At our last staff meeting, I was understandably excited to see for my first time a book that claims to be aligned to the common core state standards (Algebra 2 – Glencoe/McGraw Hill). I reviewed the book for the last three days and …what a huge disappointment!
A serious concern is that, in this book, some of the CCSS standards are missing either in body or in spirit. Here is an example. F-LE1 wants students to “[d]istinguish between situations that can be modeled with linear functions and with exponential functions”. The key in this standard is to distinguish between quantities that grow by equal differences over equal intervals and those that change at a constant rate per unit interval. In my opinion this is an important concept – it goes to the fundamental idea that functions model real phenomena in nature and that these phenomena represent various rates of change – linear, exponential (both growth and decay), zero and so on.
Not only is F-LE1 not in the book’s index of standards, but the concept of constant rate growth is stressed in the section on series, not in that on exponential functions. There is no connection established in the book between exponential functions and geometric series and the two are separated by 3 chapters (1 – 2 months worth of school days) so the idea of exponential growth is likely forgotten by the time students get to geometric series.
Here is another example. Standard A-CED.4 wants students to “[r]earrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.” Again this is an important concept, especially for those who later go into engineering, math or the sciences. In my experience students have difficulty with this – they are not trained in middle school to manipulate abstract variables.
Standard A-CED4 appears twice in the book’s index of standards. The first time it appears in the section introducing circles, but the rearranging of formulas here is not in the same spirit as Ohm’s law example – it has more to do with completing the square. The second time the standard appears is in the discussion of geometric sequences and series and again I fail to see how this standard is applied in the spirit it was written. Therefore, for all practical purposes, the standard is missing.
It looks like the standards were fitted to the book, rather than the book written around the standards. Perhaps this is not surprising, given that 7 authors of the previous book’s edition (non-CCSS) are also the authors of the new one. From a business point of view it’s good to be early in the market in response to a market need – unfortunately this product leaves a lot to be desired.
In my next post I will address the rigor of the book and how it compares to other texts (domestic and international). For now, I am concerned that standards which aim to be rigorous and indeed world-class will be watered down by textbook publishers and possibly by those that write the state exams.