As a math teacher, it can sometimes be difficult to think of ways for students to generate and test their hypothesis. In the book entitled Using Technology with Classroom Instruction that Works, one of the recommendations mentioned was problem solving (Pitler, Hubbell, Kuhn, Malenoski, 2007). In math, my department consistently incorporates problem solving in every lesson. This can be in the form of solving algebraic skill problems or solving real world word problems.
My students are currently learning the rules of exponent as well as how to simplify problems containing exponents. With the knowledge they gain while learning basic exponent rules, students may have a better understanding of the skill once we begin lessons on square roots. For instance, students will devise a list of integers that are raised to the power of two (or squared). Then, students will work backwards to devise a list of square roots. Students will generate and test a hypothesis as to what the actual outcome would be by estimating each problem. They will test their hypothesis by actually working the problem to see how close the actual answer was to their hypothesized answer.
In order to enhance students’ learning, technology could easily be utilized. According to Dr. Orey (Laureate, 2011), students should be engaged in learning and the process of creating an artifact to share with others to follow the theory of constructionism (Laureate Education, Inc., 2011). For this particular lesson involving exponents and square roots, students could create a spreadsheet via Microsoft Excel. Students could design a table with the problem in one column, their hypothesis in the next column, the actual answer in another column, and the last column would involve the difference from their hypothesized answer and the actual answer. Then, students could create a line graph that represents the difference from their hypothesis and the actual answer. This way, students can visually see how off or how close they were to generating the correct answer for each problem. After generating their graph, students can share their findings with their collaborative groups. Students can compare their differences and distinguish which problem(s) the majority of students were missing. Finally, collaborative groups can work together in order to formulate a plan for determining the correct solution to those problems which had the most errors.
Laureate Education, Inc. (Producer). (2011). Program five: Cognitive learning theory [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from http://laureate.ecollege.com/ec/crs/default.learn?CourseID=5700267&CPURL=laureate.ecollege.com&Survey=1&47=2594577&ClientNodeID=984650&coursenav=0&bhcp=1
Pitler, H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD.