Anchored Instruction in the modern mathematics classroom

As a high school math teacher, I was excited to read about the Jasper series and think about how it could have been implemented today. Although the concept of TPCK did not exist back in the 1980s when the series was first introduced, it was clear that teachers that wished to teach using the series had to have had experience working, and teaching with technology (needed to know how to use a video, and teach students how to learn from it). If the same series was used today, I can imagine that students would have been able to view, or construct the problem in a multitude of ways:

1.Video, or VR simulations – When Rescue at Boone’s Meadow was first introduced, the problem was given through video, with the Cognition and Technology Group at Vanderbilt (1992) suggesting that the video based format increases motivation, and allows the videos to be searched much more easily. One can imagine that such a scenario be delivered using modern day simulation technology like VR that could allow students to live through the problems. One can also imagine being able to simulate their solution through virtual reality. Although this technology is still undeveloped, we are pretty close to seeing VR entering the educational realm in full force.

The concept of teaching with video is widespread in today’s education system, especially for mathematics. Many YouTube channels, such as the Khan Academy, offer a variety of mathematical tutorials, and lessons that students utilize in order to learn concepts independently from school. As a teacher though, I believe that if one were to utilize videos effectively, one would often have to rely on videos produced by other teachers, as the time and resources required to create a video of high quality is often too much for a single teacher. As a result of that, the instructor must always adapt their teaching style or methods around what is seen in the video.  This is not a tremendous issue, but when teachers use videos, they are often placed in more of a facilitator role, as opposed to being more direct with their teaching. Although this is encouraged in many modern research, indirect teaching may be resisted by certain students.

2. Online discussion of solutions – Rescue at Boone’s Meadow was introduced before the internet era, and as a result, discussions around solutions would take place synchronously in a classroom across a couple of periods. However, in today’s internet age, one could imagine online resources in playing a large role in influencing students development of a solution. Just like a video game, students across the country could pick apart, and dissect the situation faced by Jasper in the scenario, and naturally, multiple feasible rescue methods are likely to be found on the internet. If students were resourceful and found these solutions online and used them to develop their own solutions, how should teachers assess for student learning?

In terms of modern mathematical tools such as CTC math, IXL, etc. I believe that many of these tools seem to oppose anchored instruction, and the more popular these tools get, the farther we deviate from the design principles discussed by the Cognition and Technology group at Vanderbilt.  Tools like IXL have their place on mathematics education in that they offer students an excellent resource to practice skills that can learn through repetition (for example, arithmetic, algebra, equation solving), but they often offer very one dimensional ways of delivering information. Anchored instruction relies on linkage across curriculum and student independence in formulating their own problems and solving them, whereas online tools such as IXL do the opposite, they create all the problems for the students to solve.

 

It would appear part of having a strong base of TPCK is knowing when to utilize technology, and understanding what the benefits are consequences are when we adopt a new software for the classroom. We can introduce students to IXL and Mathletics and encourage students to work on problems, but sometimes it takes time away from giving students situations like Rescue at Boone’s Meadow, where a large emphasis is on discussion and generative problem solving. An expert will need to properly balance both teaching activities in the classroom.

 

Barron, L., Bransford, J., Goin, L., Goldman, E., Goldman, S., Hasselbring, T., … & Vye, N. (1993). The Jasper experiment: using video to furnish real-world problem-solving contexts. Arithmetic Teacher, 40(8), 474-479.

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.

3 comments

  1. Thanks for your great ideas Gary! I was really intrigued by your explanation of using VR to present problems similar to the Rescue at Boone’s Meadow. It certainly would enhance student motivation. What a neat idea it would be to have students interact with the problem itself in the virtual world as well. It would provide them with immediate feedback, allowing them to alter their decisions towards solving the problem as they went. I only wonder how the collaborative aspects would be, if there would be any. One of the key aspects of anchored instruction, constructivism and the goals of the Jasper series is to have students learn from one another. Although, as you mentioned, the online discussion forums may present a synchronous solution to collaboration, if students are plugged into a VR headset, that element may be removed. This is all in speculation of course, since we’re still a little ways away from having this technology available in schools. Just something for us as teachers to consider when the time comes…

    Thanks again!

    Jocelynn

  2. I agree Gary, that I think VR will soon play a key role in our classrooms. I remember my brother showing me Google Cardboard and an app that let you travel on synapses in the brain to see how a message gets from one place to another. It was incredibly cool. As the technology does become available in our classrooms it will certainly cause yet another shift as we evaluate how to use it in meaningful ways. I was introduced to the SECTIONS model by Bates (2014) in 565A and I find myself returning to it as a framework to start to evaluate any technology I bring into my classrooms. It provides a way to look at practical things like cost to bigger picture ideas like teaching functions, what pedagogy are you supporting with this technology use.

    References:
    Bates, T. (2014). Choosing and using media in education: The SECTIONS model. In Teaching in digital age. Retreived from https://opentextbc.ca/teachinginadigitalage/part/9-pedagogical-differences-between-media/

  3. I really liked your idea about delivering learning scenarios using modern day simulation technology like VR, Gary. My take on the evolution of the technology is that it will not only allow for exceptionally well constructed, rich learning scenarios but also for the potential to offer students hints of how a learning scenario can evolve. With traditional methods, most concepts are taught in isolation, e.g. Math concepts are not immediately applied to target domains like business or sports; it is difficult to construct such rich context. However, with VR, and some competing technologies like Augmented Reality (AR), it is now possible to present a learning concept as story or a game that is constantly unfolding, engaging students to apply new concepts in progressively more difficult and emerging scenarios.

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