Sunday, March 6, 2016

Give Students the Tools needed to Solve Problems...

In my previous blog, Questions that Spark Student Curiosity, I discussed ways to ask questions that would engage students. France Snyder commented, “What is the best way to evaluate our students? What is the effect on our students’ engagement, retention, and transference of skills? What is overall best for our students?” I’ve thought a lot about how we evaluate students over the past few weeks, as we have just completed first semester final exams. 
While prepping my students for their final exams, I fielded questions  from students about how to access the study guide, the best way to study at home, and how many class periods would be dedicated to finals exam review. My response was consistent with past years.  “Every one of you is aware of what we discussed in class.  You are also aware of how to access the resources we used in class.  To study for the final exam,  consider our conversations and reflect on them.”
When the final exams came, I chose to spend an extra day administering the exam over two full hours so students could consider their responses thoughtfully without time constraints.  After I distributed the exam on the first day, students responded “It’s only 8 questions.  Why would it take 2 hours to complete?”  Shortly after exams were over and students had a chance to reflect, I asked them what they thought of the exam and their responses reaffirmed my final exam strategy.  “It wasn’t hard but my answers were not the same as those of my friends.  We knew you would not accept a simple ‘yes’ or ‘no’ so we really had to think about all the options and justify our responses.
To me, final exams aren’t for the sole purpose of determining what knowledge a student has attained and what facts that student has memorized.  They are an integral part of the learning process.  For many decades, we have asked Webb’s Depth of Knowledge (DOK) 1 and DOK 2 questions: those questions with a single correct answer that leads students through a single path of thinking.  Now, we are focused on  DOK 3 levels of thinking, so we know there is a better way to evaluate student learning.  Yet, we still fall back to the familiar ‘yes’ or ‘no’ style of questioning in many of our final exams.
I was on Facebook the other day and saw a post that made me stop and smile.  “Don’t ask kids what they want to be when they grow up but what problems they want to solve.”  This is a perfect example of changing a question from a one-word DOK 1 answer to a thoughtful, considerate DOK 3 response.  What problems do we want our students to solve?  I don’t want them to solve a problem in which the answer is known.  We need to stop training our students to accept DOK 1 questions as the norm.  Life doesn’t contain these simple problems, and neither should education.  Any question that ever told me anything about a student was a question I didn’t know how they would answer it and more importantly, how they would explain their answer.
While working with one of my teachers responding to an email from a disgruntled parent about the lack of “math” being taught we decided to dig a little deeper.  The parent described how he retaught his daughter using proper math and how she now completely understands everything we were trying to get through to her.  We did what any good teachers would do.  We asked her to explain her understanding.  She could explain parts, but after a few steps, she could not explain the next procedure and, most telling,  couldn’t explain her goal.  DOK 1 questioning that we have been doing for years promoted a recipe style of mathematics.  Our students don’t retain it and, most importantly, they don’t like it.
Webb’s DOK is not just a method of questioning for the sake of questioning.  It is a way to help students attain a higher level of understanding.  At the same time, it is a method that encourages student engagement.  Encouraging students with questions that make them consider multiple options and different perspectives to solving mathematics will only aid them in enjoying what they are doing, which in turn will make for better mathematicians.
It’s not about just teaching for recitation.  It’s about giving students the tools to solve the problems they want to solve.

Walter Wick bringing a New Perspective to Math...

On a Sunday afternoon that the family finally had a free moment, my wife took the family to the Woodson Art Museum to view the Walter Wick exhibition. Walter Wick is the photographic illustrator of the I SPY series, and the author/illustrator of the Can You See What I See? series.  Besides see some amazing photography and reflecting on a bit of my own past, I had so many moments of game changing instructional opportunities.  balancing act

The first came from a pair of photos called Balancing Act, of which one is pictured at the right.  The photo shows many objects seemingly placed at random all balancing on a single piece of LEGO.  Mr. Wick mentions the process of getting everything to balance took over a week with much trial and error and several crashes along the way.  What I saw was the amount of math that could be extracted and then performed from such a starting image.  From 7th grade ratios and proportions to symmetry all the way through the upper levels of mathematics.  What intrigues me the most is that almost every student will have objects similar to these sitting in their home.
Slide-SortingClassifyingNext to this photo was another called Sorting and Classifying from the I SPY School Days.  From my experience teaching Geometry to planning earlier math lessons the concept of a Venn Diagram is not the easiest concept to grasp when applying it to mathematics.  However, what if the class started with a photo of Sorting and Classifying followed by the simple question, "What is the purpose of the rings?"  Instead of teaching students what the Venn Diagram is, allow students to discover its' purpose and what they sort in this situation.

The final photo thatmirrorsI felt it was important enough to share is Mirror Maze.  This photo is created by using mirrors in the shape of an equilateral triangle to make the maze.  I sat in front of this photo for at least 15 minutes just following the reflections and identifying where I felt there could be inconsistencies while also looking for justifications of the inconsistencies.  This is the type of thing that would make Geometry much more intriguing.  The number of places it could fit in during the year is almost limitless.

All these are just pieces to a puzzle I have been trying to solve in my head and in the classroom for some time.  Students have a limitless amount of stimulus throughout the day that take their attention away from the classroom.  However, rarely do they find something that they could just stare at and be intrigued.  The other piece to these photos is not only the depth of the mathematics but the access to many other levels of math.  For example, most of a typical Geometry course could be made up with just these three photos and connecting the concepts between them.

My thoughts now settle on the art that I am missing to further enhance mathematics.  On a side note and for our M.C. Escher enthusiasts.  Check out Going Up and Tricky Triangle.  These are not drawings, which often lead students to find M.C. Escher "cool" but not with the same curiosity as something real.  These are photographs of real objects.  Go ahead and find the intrigue.
paradoxical pavillion                                                   IMG_1254