Monthly Archives: July 2011

Understanding by Design!

We had a school workday today, and our guest facilitator gave us a quick overview / review of Understanding by Design, a sort of “backward planning” process.  You plan a unit by first defining your student learning objectives, then writing essential questions, then planning your assessments, and then planning individual lessons / activities to support all of the above.  It’s something all teachers learn in their university course of study, but the review was helpful.  I actually had been skipping the “essential questions” part of the planning, but overall following the process with my colleagues.

I decided to make use of the time by re-designing one unit that had given me poor results in the past couple of years.  I met with our math department coach and another teacher who teaches the same course, and we started in with UbD (as it’s called).

The course is Connected 2 Accelerated, which is also known as seventh-grade pre-algebra.  We started assigning almost all seventh-graders to this course last year, so the range of abilities in the class is very broad.

The unit is “Comparing and Scaling”.  This is the second unit we teach during the course.  It covers a lot of material and is going to cover even more this year, thanks to some newly revamped standards courtesy of our state department of education.

In a nutshell, we go through percents, fractions, decimals, rates, ratios, and estimation skills.  It’s a very broad unit and it’s usually broken into two parts because it takes so long.  It’s a struggle, I won’t lie.   It is supposed to build strong number sense about these concepts, but it hasn’t come easily in past years.  Students end up learning tricks and procedures, but the knowledge seems quite fragile and the deep understanding is weak.

We got as far as unit objectives, essential questions, and the start of a rubric for grading an assessment.  I was really intrigued with the essential questions.  These drive inquiry, and I feel rather proud of what my colleagues and I came up with.  If I can design lessons that really get at the essential questions, we could have a unit that really has deep thinking in it.  Here’s what we came up with.  Supposedly, they’re good ones if they make the reader start wanting to answer them 😉  What do you think?

Essential Questions for Comparing and Scaling:
– When is a big number not actually so big?  How can you tell a small number is small?
– How do number comparisons influence your decision-making?
– How do you communicate numbers so your audience appreciates what is important about them?
– How can you tell if you have made a good prediction? What information is needed to make predictions?

Our school uses standards-based grading, which means part of my unit plan must include what we define as “proficient” work – and then “advanced” work and “partially proficient” work.  The “proficient” is reasonably easy to define, as I have a good sense of the kinds of problems kids should be able to solve in this unit.  Advanced is much more difficult. How do you go beyond expectations in solving problems with, say, percents?

Once my colleague and I have a draft of the rubric and goals, I’ll post it here!

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Posted by on July 29, 2011 in Uncategorized


A little background

You might have heard of TIMSS, the study that lays bare where the US ranks in terms of science and math education – and hypothesizes some possible reasons for our low placement.  One part of this study was a video study of math and science lessons in the US and other countries around the world.  The video study showed that in countries where students perform well in math, the way math is taught is fundamentally different.  Lessons involve more open-ended questions, more teaching of problem-solving, less teaching of procedures and memorization.  Students get through fewer problems and work through them more deeply.

Over the summer, I read a book published by the NCTM: Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development by Stein, Smith, Henningsen, and Silver.  The dry title doesn’t do justice to what is a fantastic book.  It’s a handbook for teaching in the way the TIMSS study recommends, and it’s a very accessible book, written in the form of case studies from many different lessons presented by different teachers.

I devoured the book and determined that I would do my very best to step up my teaching style – to present lessons in a way that would have a higher cognitive demand, more challenge, more depth.

The book suggests categorizing student tasks by cognitive demand.  I’m going to steal just a little and write the example given in the front of the book that they use to demonstrate the four levels.

Memorization  (example:  give the decimal and percent equivalents for 1/2 and 1/4.)

Procedures without Connections (example: Convert the fractions 3/8 and 4/11 to decimals and percents.)

Procedures with Connections (example: Use a 10×10 grid to show the decimal and percent equivalents of 3/5.)

“Doing Mathematics” (example: Shade in 6 squares of a 4×10 rectangle. Using the rectangle, explain how to determine the percent of the area that is shaded, the decimal part that is shaded, and the fraction of the area that is shaded.)

The book then goes through a series of lessons with reflections written by teachers, and discusses the cognitive demand of the lesson and factors that contributed to the cognitive demand.  At times, a lesson can start as a high-cognitive-demand task, but as the lesson progresses and conditions deteriorate, students find themselves doing tasks with less and less cognitive demand – due to one or more factors.  A task may be inappropriate for a student’s background knowledge.  The teacher may not manage his or her classroom effectively.  The teacher may answer questions so completely that he or she ends up teaching a procedure and not problem solving.  Questions may not be appropriate for the level of cognitive demand.  It seems to be very tough to start, see through, and finish a task that has a high level of cognitive demand.

I would like to learn to do it well.

I’ll reflect on the lessons I try here, and use this blog as a tool for improving the way I create a problem-solving environment in my classroom.

I will also post the awesome things that seventh-graders say in response to my best efforts to teach them.  🙂

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Posted by on July 27, 2011 in School and Unit Planning