Maverick Mathematics

As we continue reading Building Thinking Classrooms, we are now exploring the use of scripted curricular tasks.

Scripted curricular tasks have three parts:

1. Posing a question about prior knowledge
2. Asking a follow-up questions that extend on prior knowledge
3. Asking students to do something without telling them how

This three part approach allows students to incrementally gain success by connecting back to previous learning and by problem-solving together to discover a new concept. When scripted curricular tasks are well-planned, the learning is seamless and the students are given the opportunity to take ownership of the new ideas.

In Algebra II, our students explored how to factor a trinomial through the use of a scripted curricular task. The lesson began with students competing in a puzzle rush competition that required them to determine factors that would multiply to get a particular number and add to get another number. This activity connected to their prior knowledge of factors and their general number sense. They were then asked to multiply two binomial expressions using a graphic organizer that reinforced the concept of "like terms." This activity extended the numerical focus to an algebraic one. The students then worked in small groups at whiteboards around the classroom with the challenge of determining the binomial factors given a trinomial. The students did an excellent job determining the factors. They then collaborated on a series of problems that increased in difficulty. The lesson ended with the students completing an exit ticket that required them to determine the errors in 4 different solutions to a given problem. The lesson was a great start to their experience with factoring trinomials.

AP Calculus AB students also experienced a scripted curricular task when they were asked to apply the limit definition of the derivative to develop the Power Rule for derivatives. The students first looked at a constant function graphically to determine that the slope of the tangent line is zero. They then applied the limit definition of the derivative to several functions of the form f(x)=x^n and were asked to observe any patterns that occurred in their work. They quickly discovered the rule and were able to apply it to several polynomial functions. They extended the lesson by applying the rule to finding the tangent and normal line of a given function.

The majority of the lesson was completed in small groups at the whiteboards around the classroom. Having students at the whiteboards opens up the classroom to collaboration. Students can observe other groups and migrate to other groups to ask questions and to check work. It also creates an environment where students focus on actively working and thinking about mathematics. At the end of the lesson, the students returned to their seats in the classroom to work with the teacher to consolidate their thinking and apply it to one final question that they could include in their notes. The lesson showed them how learning the limit definition of the derivative gave them a tool for discovering the derivative rules that they will apply throughout the year.

Our mathematics classes have been buzzing with mathematical discussion. When you visit mathematics classes at Eastern Tech, you will observe students working in small groups at vertical whiteboards around the room. This is part of a new initiative in the mathematics department. As a department, math teachers have been reading Building Thinking Classrooms in Mathematics by Peter Liljedahl. The goal of our book study is to increase student engagement and encourage critical thinking.

In his research, Peter Liljedahl discovered that students often do what is called "studenting" rather than thinking in mathematics classrooms. Studenting behaviors can range from mimicking the teacher's work to stalling until the teacher goes over the problem. The pie chart below shows the five common studenting behaviors that occur in traditional mathematics classrooms. Our goal is to create an environment that encourages students to actively engage in doing math rather than just mimicking and pretending to do math.

The video included below shows how the 14 strategies for enhancing learning from Building Thinking Classrooms have been implemented in a high school. We are currently focusing on 3 of the strategies: utilizing scripted curricular tasks, creating visible random groups, and working problems out on vertical non-permanent surfaces.

I have been teaching mathematics and computer science for 25 years at Eastern Tech. I am highly dedicated to our students and our school community. In 2009, I was awarded the Presidential Award for Excellence in Mathematics and Science Teaching.

Email: kburton@bcps.org
Website: www.theteachingtea.com
Location: Eastern Technical High School, Mace Avenue, Essex, MD, USA
Phone: (443)809-0190
Twitter: @ETHS_Math