Unit 3: How do I Generate Problematic Tasks?

Unit Objectives

1. The learner will analyze two problematic tasks writing their thoughts in a reflective journal.

2. Using the provided resources, the learner will generate in writing a problematic mathematics task or change an existing traditional task to a problematic task.

3. The learner will choose to adopt Problem-based Learning by incorporating problematic tasks into their classrooms

How do we Create Authentic Mathematics Learning Environments?

Read Creating Authentic Mathematics Learning Contextsfor helpful tips for creating and implementing authentic mathematics contexts in your classroom.

After reading the article, reflect on the following questions in your jounal:

1) What contexts could I incorporate into my classroom that are meaningful to my students?

2) How can these contexts help to reach better understandings in mathematics for my students?

3) Which mathematical concepts could be taught using an authentic context?

Authentic Mathematics Contexts

Watch two lessons from either Public Lessons or Number Talks and using your knowledge from the above article, reflect on the following questions, taking notes in your journal for later use:

1) What contexts were incorporated into the lessons that interested the students?

2) What specific mathematics concepts were taught during these lessons?

3) Were the students more interested and motivated in the lesson itself because of the methods used to teach the concepts than you may have experienced teaching these same concepts?

Generating Authentic Tasks

So far in this lesson, you have read an article that discussed key components in creating authentic contexts for your students and have watched such contexts being implemented. Now it is time to create your own authentic task for your classroom.

♦ Chose a topic, mathematical concept, or task you use in your math classroom. For more ideas of concepts and quick examples of concepts that can be used as authentic tasks, please visit "Classroom Examples" on page 3 of Problem-Based Learning in Mathematics

♦ Read the reflections in your journal or revisit the characteristics of a problematic task discussed in Unit 2, and list at least two ways you can make your mathematical concept/task more problematic in nature.

♦ Finally, generate your task, highlighting the key features of the task in your journal that make it a true problem, as described in Unit 2.

Resources

"Creating Authentic Mathematics Learning Contexts." The University of Kansas. Web. Sept. 2012. <http://www.specialconnections.ku.edu/?q=instruction/mathematics/teacher_tools/creating_authentic_mathematics_learning_contexts>.

MacMath, Sheryl, John Wallace, and Xiaohong Chi. "Problem-Based Learning in Mathematics." What Works? Research into Practice. The Literacy and Numeracy Secretariat, Nov. 2009. Web. Sept. 2012. <http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/WW_problem_based_math.pdf>

Number Talks. Inside Mathematics. Web. Sept. 2012. <http://insidemathematics.org/idex.php/number-talks>.

Public Lessons. Inside Mathematics. Web. Sept. 2012. <http://insidemathematics.org/index.php/classroom-video-visits/public-lessons>.