It has been said for many years. "I'm not sure last years teachers did such a great job. Students don't even know (fill in your major topic that students should remember from a previous year)." Teachers had very little way of fixing this without practically going to last years teachers and accusing them of poor instruction (Even though this is an extreme situation it is far from uncommon).
Maybe this doesn't have to be the case anymore. The Common Core State Standards have had many advantages in the classroom. The most prominent may be a basic set of expectations that all teachers at a specific grade level should see in their classrooms. This base-level has made it possible for sites such as http://jeffbaumes.github.io/standards/ to make retention more than just a lucky happening. Not only does this site show clearly what standards your current instruction will lead to but easily identifies the "end" of a topic. It also has the ability to identify those topics that make one think...why do we need this taught at this grade level?
After spending a while looking at the matrix, many of the standards I question happen to be Geometry standards. For example, 5.G.4 asks students to classify two-dimensional figures. Often, this is discussed in High School Geometry where inevitably we hear the words from teachers claiming students should know this "stuff" already. Should they? If we teach Geometry in 10th grade and the last time properties of 2-dimensional shapes is mentioned is in grade 5, a full half-decade earlier...should they remember? The same argument could be made for angle measurement, another common topic in 10th grade Geometry. Prior to Geometry the last time it was mentioned in the standards was in 4th grade. Using a protractor is such a foreign tool to begin with. Since it doesn't come up again until the 10th grade it makes sense that students struggle with what is perceived as a very basic task. Instructionally this begs 2 questions, the first of which I would rather not tackle.
Why is this topic in the grade if it not important enough to expand on for 5-6 full years?
How can this help us form instruction to enhance retention?
This site makes it quite easy to see what leads into your current topic (provided you are teaching in K-8). Take for example 7.G.2. This standard has no prior skills attached to it. Therefore we know that all the vocabulary is new, all the concepts are new, and that we clearly need to attack this standard from step #1. Taking a different perspective 6.EE.3 discusses the distributive property. Any elementary teacher will tell you how often the distributive property is instructed, used, discussed from multiplication algorithms, to area models, and many more concepts. The site confirms this. In 6th grade the teachers role should be to access its previous uses and expand on them working their way into algebraic expressions.
In education, too often we get caught up on the goal. Sometimes it makes more sense instructionally to look at learning from the students perspective and ask some important questions.
When was the last time this topic was discussed?
What was its context?
How can I expand on that context to tie it to the new standard?
It is those types of connections that make instruction effective. So thank you Jeff Baumes and Jason Zimba for your work on the dependencies in mathematics. Hopefully we can make effective use of your time.
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