Education week recently wrote a glowing article describing a group of hard working and dedicated teachers in Utah who were writing curriculum to promote the Common Core Standards. I absolutely agree with the teachers that many textbook companies are repackaging the same materials they developed before the Common Core Standards without substantially changing the content. Given that even white students who had at least one parent attend college in our highest performing state still fall woefully behind when compared to all students in other countries in math achievement, it is clear that traditional math instruction is not working. Analysis of International Math Test Data
I absolutely understand why the teachers in Utah felt like they needed to create their own curriculum and I appreciate that they included a number of interesting problems in their online textbook. However, given that they are full-time teachers who are writing it on the weekends, and are immersed in the culture of a country with poor math achievement, I do not think that they are in a position to create a quality product. However, their book is online, and they plan to edit it and learn from their mistakes, so given the right assistance and time to reflect and change this book could be good. Their hearts are in the right places but they do not have a lot of positive examples of high quality curriculum and instruction to look at for inspiration.
For example, they have the great idea of giving kids links to videos which explain mathematical concepts instead of writing explanations of mathematics in the book. If high quality videos of mathematical instruction could be found online, they could easily be appended to the book, and the students would benefit from the video. However, in practice, most of the videos of instruction that I have found online display little sensitivity to student thinking or knowledge of how students learn mathematics. Often the videos teach kids how to get a correct answer but not how to understand what mathematics means. The wildly popular Khan Academy has even been criticized for not even explaining traditional math clearly. Personally, I find it depressing that someone with no background in student thinking is the most popular teacher in the country. Every time I watch a video of his I find something that could be improved if he had studied how kids learn math. I’ll give an example of what I mean in my next post.
Furthermore, the Teaching Gap provides copious evidence that almost no mathematics lessons are high quality in the United States. Even teachers who are hard working and intelligent do not have someone to observe if they want to look for meaningful instruction. The study in the Teaching Gap took a large random sample of teachers in three countries, taped their classrooms and transcribed the interactions. Experts rated the instruction as Poor, Average or Good without knowing which country the tapes came from. Not one classroom lesson from the United States was ranked good, with 93% being ranked poor. Japan, on the other hand, had a majority of lessons ranked Good or Average.
I find evidence of these findings whenever I look at videos of teaching online. For example, this post describes a teacher who was applauded for teaching a great lesson about a Common Core standard. The problem was that she taught a quick procedure that had the same word in the name as the standard. She didn’t actually teach the standard in the video and nobody noticed when it was put up on a popular teaching website.
Even though the book written in Utah has some good applied problems that might promote sense making, they basically rehash common problems found around the country for most of the book. In the next post, I’ll describe how their problems on rate of change could be improved and give evidence from my own research on math teachers and Calculus students that the current approach to slope doesn’t promote meaningful understandings that can be used in science and math in college. I’ll also defend my position on Khan Academy by showing how his lesson on slope promotes a meaning for slope that is problematic and incoherent.
If these hard working teachers had a source of quality problems written by someone with an understanding of how kids learn math and videos that promoted meaningful, quality mathematics their book would probably be a great success. Lacking those resources, and without the time to read research on student thinking, the teachers are basically set up to repeat the mistakes of the past and produce something that is fundamentally a product of our broken mathematics culture.