Allowing students to construct their own understanding of concepts in a manner that does not lead to the formation of misconceptions can be very difficult. The Jasper materials are aimed at taking students beyond being able to produce facts and show competency in a set of prescribed skills; the focus is on helping students to use facts and skills to solve problems.
I strongly believe students only learn that which they have constructed for themselves. Mathematics and scientific disciplines, that require a greater amount of application of knowledge, prove to be more challenging to students who lack conceptual understanding because they must go further than simply regurgitating information. The other issue is that misconceptions tend to be more commonplace and harder to correct when students have not properly constructed the concepts for themselves. Solving these issues can only be tackled by using methods that show students how to go about constructing understanding for themselves; it is a skill that has to be learnt.
A problem-solving approach to tackling the issues discussed has been debated in the literature. There are those who agree that approach builds on constructivist principles (Tandogan & Orhan, 2007) and will therefore help students to develop a conceptual understanding that is less prone to misconceptions. On the other-hand some researchers argue that a problem-solving approach does not provide enough guided instruction and can even setback students especially if do not possess sufficient knowledge base to approach the problem (Kirschner, Sweller, & Clark, 2006). However, as Hmelo-Silver, Duncan, & Chinn (2007) have shown the problem-solving approach is not minimal guided instruction but it requires that students are scaffolded properly with appropriate guidance.
The Jasper materials use videos to provide students with information that they will use to solve stated problems. The approach requires students to derive a method for solving the problem and then to find the information required by searching through the videos. The process requires students to take a generative learning approach and they are encouraged to do so working in cooperative groups (Cognition and Technology Group at Vanderbilt, 1992). Students have to create their own structure of the problem and what variables they need to know solve it. As the researchers of the Cognition and Technology Group at Vanderbilt have pointed out, the process because it requires reasoning and reflection is better at tackling misconceptions. The cooperative learning aspect helps students to be focused on the issue at hand and not to go too far down a wrong path.
In what ways do contemporary videos available for math instruction and their support materials
The contemporary videos that don’t necessarily offer a problem-solving approach to the teaching of the concepts. The videos are engaging, and they also tend break-down concepts so that they are more easily grasped but they don’t require students to develop their own schematic approach to solving the problems. The primary method for assessing our students is the use of tests that are aimed at assessing their ability to master curriculum-driven content and skills. The videos are therefore designed to meet those needs.
References
Cognition and Technology Group at Vanderbilt. (1992). The Jasper experiment: An exploration of issues
in learning and instructional design. Educational Technology Research and Development, 40, 65-80.
Hmelo-Silver, C. E., Duncan, R. G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based
and inquiry learning: A response to Kirschner, Sweller, and Clark. Educational Psychologist,
42(2), 99-107.
Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not
work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and
inquiry-based teaching. Educational psychologist, 41(2), 75-86.
Niess, M. L. (2005). Preparing teachers to teach science and mathematics with technology: Developing a
technology pedagogical content knowledge. Teaching and teacher education, 21(5), 509-523.
Tandogan, R. O., & Orhan, A. (2007). The effects of problem-based active learning in science education
on students’ academic achievement, attitude and concept learning. Eurasia Journal of Mathematics,
Science & Technology Education, 3(1), 71-81.