TechGrads- Week 11 Pamela Jefferson

We held a Skype discussion to address the Week 11 questions and came to several of the same conclusions.

1. With your team, study the dimensions of divergence carefully and see if you can think of any that should be added or deleted. (It should be based on the principles for teaching each designated components, the sequence of the instructions, and the levels of complexity of the generic skill.) (Need references!).

Http://www.naturalmath.com/multmodels/3.html has a posted graphic for all of the multiplication models. According to Reigeluth (1999) the most important component of a generic skill is the procedure or set of steps used to perform the skill. The procedure for multiplication is missing from http://www.naturalmath.com/multmodels/3.html. The Multiplication Model section of the site does attempt to address the principle of multiplication by providing a visual aid to help users understand when to apply a particular model. Unfortunately, several of the multiplication models provided are not good representations of the model being addressed. The memorization component is not addressed by http://www.naturalmath.com/multmodels/3.html.

          The sequence of the multiplication models presented on http://www.naturalmath.com/multmodels/3.html does not follow Reigeluth’s recommendation to begin with the easiest cases to account for levels of complexity. Users can of course click on the multiplication models in any order as the website does not function in a linear manner. http://www.naturalmath.com/multmodels/3.html begins with Scale, Stretch followed by Skip Counting, Number Line, Time & Money. If we were to begin with the simplest cases as they are introduced to students in most math curricula we would begin with Skip Counting, followed by Repeated Addition, Sets, and Arrays. Presenting the multiplication models in order of the simplest case would reinforce student’s intuitive models of multiplication as found by Mulligan and Mitchelmore (1997). Mulligan and Mitchelmore (1997) found that second and third grade students used direct counting, repeated addition and multiplicative operation as the intuitive models when solving multiplication word problems.    

Reference

Mulligan, J. T., & Mitchelmore, M. C. (1997). Young children's intuitive models of multiplication and division. Journal for Research In Mathematics Education, 28(3), 309

Reigeluth, C. M. (2012). Module 7: Generic Skills. Retrieved April 15, 2012, Retrieved from http://www.indiana.edu/~idtheory/methods/m7c.html

2. Look at the components of the generic skill for this review. How the procedure was presented – a set of steps, an important list of principles, or an un-organized laundry list? Multiplication is never presented on Natural Math as a set of steps or list of principles. The multiplication models are just presented as a set of posters that can be used as a visual representation of each model. There are no steps, directions, or procedures.

3. Identify the cognitive, affective, and behavioral aspects of the attitude you found from this Group Critique I site. (Need References.)

The cognitive, affective and behavioral aspects of attitude make up the three components of engagement. According to Linnenbrink and Pintrich (2003) self-efficacy, a student’s belief that they can do something, results when there is behavioral engagement, cognitive engagement and motivational engagement (affect). It is their belief that self efficacy leads to more engagement which leads to more learning and increased achievement. Because there are no interactive elements on Natural Math I do not think that students would find the site engaging. Research conducted by Yang and Tsai (2010) showed that students that use technology in mathematics learning have more positive attitudes toward mathematics than those that did not. This suggests that the positive attitude students have about using technology can help focus their attention on learning mathematics.

Reference

Yang, D.C., & Tsai, Y.T. (2010). Promoting sixth graders' number sense and learning attitudes via technology-based environment. Journal of Educational Technology & Society, 13(4), 112-125.

Linnenbrink, E. A., & Pintrich, P. R. (2003). The role of self-efficacy beliefs in student engagement and learning in the classroom. Reading & Writing Quarterly, 19(2), 119.

4. How do you define the attitude conflicts occurred between the principles of learning and teaching? (Need references.)

Depending on the age of the students there is a potential disconnect between the content on the multiplication models, which may be the reason for a teacher’s desire to use the site, and the students perception of the material. I think that older students would balk at using a site they perceived to be designed for younger students. A negative attitude would already be in place before instruction began. Studies by Pugh and Bergin (2006) suggest that when students have a personal interest in a topic they are more likely to develop “the deep-level, connected knowledge structures needed for transfer” (p. 148). This kind of deep learning, which can be transferred across domains, will not take place if students are unwilling to take part in the experience. A teacher determining the situations and methods for instruction using Reigleuth’s Instructional Design Theory (1999), would probably find a better resource than Natural Math to introduce multiplication models.

Reference

Pugh, K. J., & Bergin, D. A. (2006). Motivational influences on Transfer. Educational Psychologist, 41(3), 147-160. doi:10.1207/s15326985ep4103_2

Reigeluth, C. (1999). Module 1: Kinds of learning. Retrieved April 15, 2012, from http://www.indiana.edu/~idtheory/methods/m2e.html