Understanding by Design

      The idea of Understanding by Design as a curriculum framework is an appealing one.  Backward Design makes a lot of sense when you read about it.  How can you start a journey if you don’t know your destination?  I was first exposed to this concept in SED 406 with Dr. Kraus and I had the opportunity to practice it that semester.  I designed a Calculus unit on limits and the first thing that was done was a unit outline.  Here we described our goals for the unit, an essential question, and what content standards we working towards.  Having the goals in mind, and knowing what I wanted the students to take with them from this unit to the next was very helpful when starting the next step of the project, which was creating the final assessment for the unit.  Then again having that test made and knowing exactly what the students would need to answer was a great benefit when creating the rest of the unit.  My examples and practice problems were designed to get the students familiar with the same problem types that would appear on the final test.  It was also very easy to make sure I didn’t leave an important point out of any lesson because I could always go back and reference the test.  If I had tried to start at day one of the unit and work through all the lessons and made the test last, I’m sure I would have had to do a lot more work going back and filling in things I left out.  This experience had led me to believe that this might be the best design option. 

            The reading’s reminders to focus on making the unit cohesive resonated with me as well.  With only 180 days in a school year there is too little time to be doing things simply because they are fun or because the students will be engaged.  The real challenge is crafting the engaging lessons out of the essential content. 

            The other important point to focus on is presenting new material in a way that relates to previously learned material.  Too often in math I find that there is a segmentation of skills.  Students do a unit on fractions for example, and when it is done they think they are done with fractions so they can forget it now.  Usually after working with fractions, middle school students move on to solving their first algebraic equations.  At this point, books will return to just using integers while introducing this new skill.  I think this goes against what we should be doing.  I have already heard from students way too many times, "You can't solve this equation, it doesn't divide evenly".  The students just learned fractions, so why not show them that this new skill has some use by having lots of fractions in the equations right away?  I think this kind of practice would help move the students towards that goal of “understanding” that these readings focus so heavily on.  I also believe it would prevent students from seeing these two units as separate entities, and a continuation of this practice would show students how every subject in math is closely related.

We quickly go from this:

To this:

And the disconnect between working with fractions and "doing algebra" begins.

          

       For me, the most interesting part of this reading was Module F on essential questions.  Even though I had made an essential question for my unit last semester I was still shaky on the idea of having an overarching question for a math class.  When I began reading this module, I was curious if they would talk about math at all or just stick to subjects like history or English.  Essential questions are supposed to “reflect the key inquiries and the understanding goals of the unit and serve to focus the unit and prioritize learning” (Module F pg. 70). This made me start thinking about what a “key inquiry” in math would sound like.  In the unit I designed, I knew I wanted the students to understand how limits shape our understanding of continuity, be able to calculate them, and see how they allow us to calculate the “slope” of non-linear graphs, i.e. take derivatives.  What I didn’t see is how this could be an inquiry.  It is a skill that can be used and a form of comprehension, but how can we have a debate about limits?  They are either right or wrong and their uses have already been established and proven.  I was glad that this issue was addressed in this reading.  The author talks about essential questions in a skill area.  Here essential questions are “not about concepts or theory but practical decision making” (Module F pg. 79).  I know now that a better essential question regarding limits could be something along the lines of “When is it appropriate to solve limits analytically to describe the continuity of a function?” or “When are limits not helpful when determining the values of functions?”.  These questions seem to be more useful to the students and result in a long term understanding and a skill they can take with them to future math courses.  Focusing on creating questions that do not just have one right answer, in a subject that is all about finding that one right answer will be challenging, but I am looking forward to practicing this skill so I can best serve my students.  I think that if my students really understand the applications and future uses of what they are learning I might even be able to change some of their minds when it comes to what they think about math.