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MMKB refers to students' "multiple mathematical knowledge bases" (Drake et. al, 2015, pg. 348). Drake et. al (2015) explains how rearranging lessons can allow students to connect the topics to their lives. He writes, "In general, the goal is to find these components that focus on (1) having students make connections between the task and their prior knowledge and experiences, (2) providing support for students to develop their own strategies, and (3) encouraging students to share and explain their strategies" (pg. 349). This is important because students can better engage with the task when they can relate it to their own lives, further developing problem solving skills.

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Chase, C. (2015, February 25). Facilitating Powerful Learning Experiences. In Creative by Nature. Retrieved April 22, 2018, from https://creativesystemsthinking.wordpress.com/2015/02/25/facilitating-powerful-learning-experiences/

Drake, C., Land, T. J., Bartell, T. G., Aguirre, J. M., Foote, M. Q., McDuffie, A. R., & Turner, E. E. (2015, February). Three Strategies for Opening Curriculum Spaces. Teaching Children Mathematics, 21(6), 346-353.

Horn, L. S. (2012). Strength in Numbers: Collaborative Learning in Secondary Mathematics (pp. 41-42). Reston, VA: The National Council of Teachers of Mathematics, Inc.

Keazer, L. M., & Menon, R. S. (2016, January). Reasoning and Sense Making Begins with the Teacher. The Mathematics Teacher, 109(5), 342-349. Retrieved from http://www.jstor.org/stable/10.5951/mathteacher.109.5.0342

Simmonds, J. (2015, April 18). Find Your Voice!. In MELBOURNE CONTEMPORARY CHOIR. Retrieved April 21, 2018, from https://www.mcchoir.com/news/find-your-voice

Turner, E. E., & Font, B. T. (2007, May). Posing Problems That Matter: Investigating School Overcrowding. Teaching Children Mathematics, 13(9), 457-463. Retrieved from http://www.jstor.org/stable/41198996

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Sometimes curriculum is set up quite well to encourage group work and problem solving, but sometimes teachers have to work with what they have, which can include outdated, rote problems. Drake et. al (2015) discusses the importance of rearranging lessons so they better encourage students to learn problem solving skills. They explain, "The key to frontloading problem-solving tasks is to engage children in those tasks before introducing a preferred solution strategy" (pg. 350). Sometimes, by simply tweaking the lesson, a teacher can better encourage student discussions and problem solving skills.

One can further adapt tasks to make them more group-worthy and involved students' MMKB.

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Part of teaching students problem-solving skills is developing skills as a facilitator. This means moving from being the teacher at the front of the room sharing knowledge, to giving students the tools to explore and discover new ideas. As a facilitator, the teacher provides guidelines on how students should collaborate and helps guide students towards the mathematical goals of the lesson. In Keazer and Menon's (2016) article, "Reasoning and Sense Making Begins with the Teacher," they discuss how teachers can remove themselves from the role of giving knowledge and can instead help students learn from each other by analyzing and questioning each others input. This is different from the traditional image of a teacher lecturing to the class.

(image below from: www.creativesystemsthinking.wordpress.com)

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When discussing my teaching philosophy, I often explain that group work is a central part of how I teach. Until this class, I did not realize the extent that the type of task matters when assigning group work. Group-worthy tasks are designed in a way to encourage participation and dependence on team members. They rely on the fact that everyone's input matters and can help others learn. In Strength in Numbers, by Llana Seidal Horn (2012) she summarizes characteristics of groupworthy tasks explaining they, "provide multiple ways of being competent in problem solving," and they should, "be designed in a way that provides individual and group accountability" (pg. 41-42). A task is not necessarily groupworthy, simply because they are labeled a group task.

One place to find a set of well-designed tasks is at: https://www.youcubed.org/tasks/

Groupworthy tasks can be designed with the perspective of "problems that matter."

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When assigning tasks in class, having students develop problem solving skills on problems that matter is important. If students can see the inherent value of a task or a type of task, they are more likely to engage and learn from it. In Turner and Strawhun's (2007) article, "Posing Problems That Matter: Investigating School Overcrowding," they discussed a task where students investigated an overcrowding issue in their school. As a result of this project, Turner and Strawhun (2007) wrote, "In general, students came to view mathematics as a tool that could help them investigate important personal and social issues. explore issues of equity and fairness, and argue and prove their point of view" (pg. 461). With tasks that students can see the inherent value and can relate the experience directly to their own lives, they can better engage with the material.

(image below from www.mcchoir.com)

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Though teaching problem solving skills is always a goal in my classroom, this class helped introduce me to strategies to begin taking steps to making my class a place where students are set up well to learn problem solving skills. There are many ways teachers can begin to better facilitate problem solving in their classrooms.