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“Technology is just a tool. In terms of getting the kids working together and motivating them, the teacher is most important.” – Bill Gates

CEP 811: Supporting My Maker Activity with Research

on July 15, 2014

The Maker Activity

Last week for CEP 811, I was challenged to go “thrifting” for materials that could be repurposed for educational purposes. Combining these thrifted materials with my maker kit (Squishy Circuits), I created a straightforward review game that will help my students practice finding equivalent fractions and decimals. The game is meant to be played in groups of about 3, and each player is assigned a specific role for the duration of each round, before switching to a new role. Roles include:

    • Problem-solver: this person will perform the math on the piece of paper that is located on the clipboard
    • Double-checker: this person will double-check the work of the problem-solver
    • Light Technician: this person will use the pointer tool to touch the negative end of the light to see which color light lights up

Students know that they’ve found an equivalency when the LED lights match: IMG_2142

“1/4” lights up green

IMG_2143

“0.25” also lights up green. 1/4 and 0.25 must be equivalent!

With my rough draft of my maker project complete, it was time to examine how my activity would hold up when compared to recent research on theories of learning.

The Research

In Richard Culatta’s 2013 TED talk, found here, he stresses the importance for educators to allow students to create something new with technology, rather than simply digitizing the old methods. Culatta elaborated on several unique affordances that technology allow, but the two that I felt applied to my specific maker activity were:

  1. Technology’s ability to provide real-time feedback
  2. Adjusting pace to fit students’ needs through the use of technology

Culatta (2013) warns against the danger of not providing feedback until the end of an assignment, for by this point, it is too late to change the cognitive processes and approaches utilized. One of the highlights of my equivalent fraction and decimal game is that it does, indeed, provide students with real-time feedback. When the “Light Technician” touches the wand to the negative end of the LED light, the group immediately knows if it is a “match” for a previously touched fraction or decimal. If the chosen fraction or decimal is not a match, the students have the opportunity to work together to discuss where an error may have been made. Students rely on their collective minds to problem solve.

In a 2007 study among adult learners taking a statistics course, T. S. Hall determined that “feedback improves learning and problem solving through facilitation of interaction among learners. When learners are able to interact with one another they share and transfer knowledge, which allows for deeper understanding of the problem and enhanced learning” (p. 84). While Hall’s study gave students feedback in a Web-based Wiki format regarding the learning of statistics, the results still apply to the equivalent fractions and decimals game, since the feedback provided can help students alter their problem-solving process and aid them in arriving at the correct answer. Hall (2007) explains, “In this process students are not graded on their initial work which may contain errors but on their continued effort to monitor and fine tune until the correct solution is reached (p. 2). In the game, students are not penalized for being wrong or for making errors. They must, however, work together to make adjustments in their approach to solving the problems through the use of feedback provided by the game.

The equivalent fraction and decimal game also allows students to work at their own pace. The game is not timed, and students can work on problems for as long as is needed. Throughout the game, students are monitoring their progress and their learning. As Bransford, Brown & Cocking (2000), explain, “A metacognitive approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them” (p.18).

Another benefit to the equivalent fractions and decimals game is that it encourages “math talk” and making sense of the problems. Xin, Jitendra, and Deatline-Buchman (2005) state, “Students with a mathematical weakness are taught ineffective strategies for mathematical problem solving such as identifying key words in word problems.” So rather than making sense of a problem or understanding math at a conceptual level, students are simply memorizing steps and trying to decide which operation to use. The equivalent fraction and decimal game promotes the use of math talk, so as not to fall into the routine that Xin, Jitendra, and Deatline-Buchman warn against.
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Additionally, Grizzle-Martin (2013) conducted a study of 24 low-achieving fifth grade students in math. Half of the students were taught mathematics using a cognitively-driven program called IMPROVE, and the other half were taught without the program. Grizzle-Martin found that out of students who were taught through the cognitively-driven program, 41.7% of them exceeded standards on the Georgia CRCT, while only 25% of the control group exceeded standards (p. 91). The implications that this study has on math classrooms is huge, for this study demonstrates the importance of metacognitive thinking. The equivalent fractions and decimals game provides students the opportunity to think about their mathematical processes in groups as they approach the problems.
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Revisions to the Game
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While I do believe that the equivalent fractions and decimals game is supported by the learning theories (metacognition, individual pacing, and real-time feedback) and by current research, there is always room for improvement and adjustment. As Bransford, Brown, and Cocking (2000) emphasize, teachers must “teach some subject matter in depth, providing many examples in which the same concept is at work and providing a firm foundation of factual knowledge” (p. 20). So instead of simply having the fractions and decimals written on the board numerically and in word form, visual representations of the fractions and decimals will also be added. This will help students to connect the visual representations of the fractions/decimals with the numerical and word forms.
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Additionally, sets of cards will be provided to further push students’ metacognitive process that Grizzle-Martin (2013) stresses, or to simply encourage deeper math talk. These cards will ask students to perform additional math tasks (e.g., “Which fractions are exactly half the value of 1/2?”), or will ask students questions like, “Pick any two equivalent fractions. Explain how you know these two fractions have the same value.” To further encourage collaboration and math talk, I am also revising one of the player roles. Instead of “double checker”, one player will be the “consultant” for the problem solver.
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Furthermore, a real-world component will be added to the cards to ask students to transfer the concepts on the game board to real-life contexts (e.g., cooking using fractions, dealing with money), for “when a subject is taught in multiple contexts, and includes examples that demonstrate the wide application of what is being taught, people are more likely to abstract the relevant features of concepts and develop a flexible representation of knowledge” (Bransford, Brown, and Cocking, 2000, p. 62).
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The person who drew the card will make the initial response, then the other two players will contribute additions, modifications, or questions based on the response. A “math talk” discussion should ensue. Once an answer is arrived upon, the group should video record the question and response on the iPad provided. (These will be viewed by teacher later, and may be used for further lessons or discussion in the future).
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Although my game is not yet perfect, it will help my students engage in math talk, problem-solve with one another, develop deeper understandings of fractions and decimals, and be provided with immediate feedback. Technology allows education to be taken to new heights, and I am excited to see what the future has in store.
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To see my revised lesson plan, click here.
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References
Bransford, J.D., Brown, A.L., & Cocking, R.R. (2000). How people learn: Brain, mind, experience and school. National Academies Press. Retrieved from http://www.nap.edu/openbook.php?isbn=0309070368.
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Culatta, R. (2014, July 14). Reimagining Learning: Richard Culatta at TEDxBeaconStreet. [Video File]TEDxTalks. Retrieved from http://www.youtube.com/watch?feature=player_embedded&v=Z0uAuonMXrg
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Grizzle-Martin, T. (2014). The effect of cognitive- and metacognitive-based instruction on problem solving by elementary students with mathematical learning difficulties. (Order No. 3617905,Walden University). ProQuest Dissertations and Theses, , 158. Retrieved from http://ezproxy.msu.edu/login?url=http://search.proquest.com/docview/1528556616?accountid=12598. (152855661)
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Hall, T. S. (2007). Improving self-efficacy in problem solving: Learning from errors and feedback. (Order No. 3307188, The University of North Carolina at Greensboro). ProQuest Dissertations and Theses, , 141-n/a.Retrieved from http://ezproxy.msu.edu/login?url=http://search.proquest.com/docview/304832899?accountid=12598. (304832899).
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Xin, Y. P., Jitendra, A, & Deatline-Buchman, A. (2005). The Effects of Mathematical Word Problem-solving Instruction on Middle School Students with Learning Problems. The Journal of Special Education, 39, 181-192.
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