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The Anatomy of a Cognitive Demanding Math Task

You all don’t have school tomorrow, I said to my fourth period class. “Can I come to school anyway?” one student shouted. I looked at him and asked why? I don’t want to deal with my parents bullshi*t! I pay bills and my parents still try to put me out.

I sat there for a second looking confused. Then I said, “You’re only fourteen.”  Another student chimed in and said, “ I pay bills too.” By this time I was way beyond disbelief.

At the end of the day, I sat down to gather my thoughts and make sense of my new found information. After a few moments, I realized that the math education that the school district provides is NOT the education that the students need.

I personally came to the conclusion that students needed less fictitious math problem solving and more real-life problems that are representative of the world since they deal with this at home every day.

What are math tasks?

Math tasks are grade level appropriate problems or set of problems that focuses students’ attention on a particular mathematical idea and/or provides an opportunity to develop or use a particular mathematical habit of mind.

They support students in making sense of mathematics by involving the use of and translation among two or more representations that deepen mathematical understanding. 

Unfortunately, according to the article, “Are Math Assignments Measuring Up?” only nine percent of math assignments they analyzed pushed student thinking to higher levels. Most math assignments were more than twice as likely to focus on procedural skills and fluency. 

The majority of the math assignments required low cognitive demand with more than nine out of ten only requiring the students to recall basic facts, perform simple procedures, or apply basic knowledge to a skill or concept. The most disturbing part is that these kinds of math assignments were more pronounced in high poverty schools.

Essential Components 

I have a student in my fourth period class who is a first generation immigrant. Every time he comes to my class, at some point during the class period he’ll say, “ I’m not going to use this in real-life anyway.”

I chuckle every time he makes this statement because what he doesn’t know is that he serves as a reminder to make my lessons and activities relevant to their lives.

Nancy Butler Wolf, the author of Modeling With Mathematics, examined math tasks These six characteristics that the math task shared were:

  1. Accessibility to ALL Learners
  2. Real-Life Tasks
  3. Multiple Approaches and Representations
  4. Collaboration and Discussion
  5. Engagement, Curiosity, and Creativity
  6. Opportunity for Extension

For the most part I agree with this list, but there’s one characteristic that most math gurus like Jo Boaler leave out in her book Mathematical Mindsets. Real-life tasks should be changed to culturally relevant real-life tasks. 

In the book, Culturally Responsive Learning Theories, “Knowing each student, especially his or her culture, is essential preparation for facilitating, structuring, and validating successful learning for all students” (Guild, 1994, p. 16). If a math task is to be accessible to all students, then it must be culturally relevant.

Before we make assumptions about students math ability, math teachers  must keep in mind, when a student is socialized in their homes differently from the school expectations and patterns, the student needs to make a difficult daily adjustment to the culture of the school and his or her teachers” (Guild, 1994, p. 19).

Learning math is already difficult but not being able to connect with the math makes the learning superficial.

Opportunities to Learn Math

If you’ve read any of my blog posts or follow me on Facebook you’ve more than likely read or heard me talk about opportunity and access. While designing cognitive demanding math tasks are important, stressing the importance to teachers about providing  opportunities for all students to work these kinds of tasks can be a daunting task.

The authors of the Culturally Responsive Educational  discuss the The Pygmalion Effect, or the idea of the self-fulfilling prophecy. In a study conducted by Robert Rosenthal in 1968 (Rosenthal & Jacobson, 1968). The study gave a group of elementary school students an IQ test at the beginning of the school year. After the test, the teachers were told that a specific group of students were predicted to excel during that school year. Eight months later, the students were tested again using the same assessment. The results showed that the group of students predicted to perform at a higher level, fulfilled that prediction.

I’ve noticed that many secondary math teachers tend to provide opportunities for students to engage in cognitive demanding math tasks based on their perception of the students’ current math ability not that they have the potential to think at a high level. 

When math teachers don’t have high expectations for students it puts the Pygmalion Effect into play. 

I am not what I think I am.

I am not what you think I am. 

I am what I think you think I am.

Teachers’ behaviors send messages influencing ways students view themselves as potential achievers or students at risk of failure. So if you’re constantly giving your students low floor math tasks then low floor students is always what they’ll be.

High cognitive math tasks are an important part of your daily routine. Whether you’re creating your own tasks or purchasing them from Teachers Pay Teachers or a textbook company check the tasks to see if they share the six characteristics identified in this blog post. Your students are worth it!

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