# Category Archives: B. Anchored Instruction Symposium

## Problem Solving with Anchored Instruction

The Jasper materials are responding to the perpetual issue of making learning relevant to our students. The Jasper program aims to show students real-life problems that require skills, problem solving, and critical thinking related to the classroom material they are encountering.

Since I became a teacher, I have surprisingly struggled with the teaching of math. This has been surprising to me because I did really well in math all throughout my schooling. In “teacher school” we were shown many new ways of teaching math that branched away from the traditional rote memorization, focusing on there being more than one way to arrive at an answer and sometimes more than one correct answer to a problem; however, bringing this teaching to my grade 3 students in a classroom setting has been a whole other dilemma. In my first year I started following the program, Math Makes Sense. This brought hands-on learning activities, worksheet practice on facts and skills, and some in depth opportunities, however, I was not making it through the units, they took forever! I felt like the only way I could get through them would be to do math all day, but what about teaching reading and writing, and then science and everything else? I have tried other programs, such as Primary Success, which provides a well-rounded curriculum of fact building. I incorporate Mad Minutes because I do see the value in continuing rote memorization of basic facts. I have tried math stations and have seen some positive correlations arise from that system. I do feel I have not encountered something that works as well as I want it too, though.

I found myself with some extra time this week due to 2 snow days (we NEVER have snow days in the Kootenays, by the way, because we are used to getting a lot of snow, but this snowfall has been exceptional!). I was quite energized after the readings and decided to use my extra time to create a set of word problems that I could use with my students. Could I get through my curriculum using problem solving incorporating multiple math topics instead of traditional unit lessons and worksheet practice? The Cognition and Technology Group of Vanderbilt (1992a) states that “students need to develop [component skills] in the context of meaningful problem posing and problem-solving activities rather than as isolated ‘targets’ of instruction (p. 66). I focused on creating these problems to anchor my instruction by making them complex, requiring significant formulation, and having multiple viable solutions that “highlight the relevance of mathematics or science to the world outside the classroom” (Pellegrino & Brophy, 2008, p. 281). I have attempted to achieve this through incorporating the names of my students throughout the problems, investigating daily issues that arise for my students, and further personalizing the problem by using pictures of my students encountering the problem. At first, I thought I would try this out with my students as whole class guided lessons. As I read these articles further, however, I grew to understand the necessity of designing this time to “scaffold learners’ knowledge construction by fostering a community of learning and inquiry,” (Pellegrino & Brophy, 2008, p. 281) as well as allowing for “extended collaborative problem solving across multiple days and multiple activities” (Hickey, Moore, & Pellegrino, 2001, p. 614).

I am very interested in the idea of Legacy projects, too. I find this partners well with my use of a class blog, as I am able to pull up pictures and video of students from previous years to showcase a similar project we may be working on. There seems to be a pull towards making a video for students, too, that is motivating and seems to draw many of them into the project as well, perhaps as the authors state, because it “helps them see themselves as part of a community whole goal is to teach others as well as to learn” (Pellegrino & Brophy, 2008, p. 293).

The readings this week and the investigation into Jasper leaves me with wheels turning towards what my possible TELE project could be at the end of this course. I look forward to continuing to explore this area.

Cognition and Technology Group at Vanderbilt. (1992a). The Jasper experiment: An exploration of issues in learning and instructional design. Educational Technology Research and Development, 40(1), 65-80.

Hickey, D. T., Moore, A. L., & Pellegrino, J. W. (2001). The motivational and academic consequences of elementary mathematics environments: Do constructivist innovations and reforms make a difference? American Educational Research Journal, 38(3), 611-652.

Pellegrino, J.W. & Brophy, S. (2008). From cognitive theory to instructional practice: Technology and the evolution of anchored instruction. In Ifenthaler, Pirney-Dunner, & J.M. Spector (Eds.) Understanding models for learning and instruction, New York: Springer Science + Business Media, pp. 277-303. http://link.springer.com/chapter/10.1007%2F978-0-387-76898-4_14

## Adventures with Jasper and Math

I had never heard of “The Adventures of Jasper Woodbury” series before this week’s section on Anchored Instruction, and while the videos are out-dated and would not necessarily appeal to students in classrooms today, I can certainly appreciate the inquiry, abstract thinking, and collaboration that the series promotes for students. While we have programs today to support these skills, many math lessons/classes continue to look more like the traditional math lessons/classes of the past with some new approaches mixed in. As was brought up in numerous posts this term, two major difficulties are the lack of teacher knowledge about programs like Jasper that could be integrated into the classroom, and the lack of training to enable teachers to integrate new programs and digital technologies. As the Cognition and Technology Group at Vanderbilt (1992) point out, “…mathematics classrooms need to shift from an emphasis on the teacher imparting knowledge to one in which students attempt to use their current skills and knowledge to approach problems to be solved (e.g., Charles & Silver, 1988; NCTM, 1989; Schoenfeld, 1985, 1989; Yackel, Cobb, Wood, Wheatley, & Merkel, 1990)” (p. 67). Rather than having teachers transfer knowledge, students must be given the opportunity to explore more abstract concepts through their own observations and experiences, allowing for a more student-centred, constructivist approach to learning. As Hasselbring et al. point out, all students “need to acquire the knowledge and skills that will enable them to figure out math-related problems that they encounter daily at home and in future work situations.”

As I learned about the Jasper Woodbury series, I kept thinking back to my time spent in learner support and about what I could do differently now, as an elementary school teacher, to help prepare my current students for secondary math when they reach that level. One thing that really struck me was the fact that I think I tend to “coddle” my students due to the difficulties they have (I have many students with learning difficulties, learning disabilities, and from very low-income homes where basic needs are often not met before they arrive at school). As I read the articles and studies, I found myself thinking about how I could incorporate more structured learning if I were to use the Jasper series (much like the structured exercises presented by the Cognition and Technology Group at Vanderbilt (1992) in Figure 1, p. 75); however, it is pointed out that “it is suspected that ‘structured problem-solving’ (Model 2) will lead to excellent mastery of the solution to the specific Boone’s Meadow problem. Nevertheless, observations of classes of students using these worksheets makes it clear that, even when students sit in groups (with one worksheet per group), the interactions among them are minimal and are confined to fact finding and computation” (Cognition and Technology Group at Vanderbilt, 1992, p. 76). In thinking more about this, I began to consider the fact that mathematics is going to be overwhelming for many students at some point in their lives. So why not give students the opportunity to adjust to this feeling of being overwhelmed in a safe, elementary environment, and to understand that they have the ability to use their individual and collective knowledge to problem-solve their way through a series of difficult, multi-step math problems, rather than over-scaffolding at an early age only to have that scaffolding suddenly removed as they get older.

While I found the videos engaging, I would be interested in finding out how students with auditory processing difficulties did with understanding information and instructions given through the videos. For myself, I found the videos that discussed topics I was familiar with (i.e., swing sets, sandbox, graphing height) were videos I could follow relatively easily. However, some of the videos that discussed details of “Rescue at Boone’s Meadow” I found myself re-watching to try to figure out the procedure. I am a very hands-on learner myself and I have difficulty with following instructions given orally. When I watched the whole “Rescue at Boone’s Meadow” video, I found there was an incredible amount of information that students would have to identify although they could replay the video as often as needed which would certainly help. However, the Cognition and Technology Group at Vanderbilt (1992) pointed out that the story was linked to “realistic problems” which would make the information “easier to remember,” “more engaging,” and would “prim(e) students to notice the relevance of mathematics and reasoning to everyday events” (p. 69). In addition to this, they highlight the fact that the video format of the series is “especially helpful for poor readers, yet can also support reading” (p. 69). Perhaps I need to stop worrying about how hard the students would find the assignments, and concentrate more on how to support them in their journey towards successful problem solving!

Today, I can certainly see my students becoming more engaged in math class if videos of a similar style were created. If I were to develop a portion of my math curriculum to align with the Jasper series, I think I would actually have students create their own videos in groups to deliver to their peers. I would create two (perhaps more) videos first to demonstrate and we could work together as a class on the first and then in smaller groups on the second. Students would then begin to plan and develop their own videos which we could rotate through groups so that each group had the opportunity to work through each peer group’s video. I think the fact that peers created videos would add to the motivation and engagement of students as they completed the problem solving each video entailed. By allowing students to experience abstract math concepts through “real-life” problem-solving situations that they had created, engagement and motivation would likely increase and students would be given an opportunity to work collaboratively with peers to address difficulties as a team, rather than as individuals.

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(1), 65-80.

Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242.

Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2006). Technology-supported math instruction for students with disabilities: Two decades of research and development. Washington, DC: CITEd, Center for Implementing Technology in Education (www.cited.org). Retrieved from: http://www.ldonline.org/article/6291/

## a problem worth solving

The Jasper series attempted to situate problem solving within authentic situations.  If I were to create my own math or science adventures, I would follow some of the same principles.  However, my main goal would be to create a problem captivating and relevant enough to my students that they would be motivated to learn something new and difficult in order to solve it.

From a Constructivist perspective, I would attempt to include confounding information that would spur students to either assimilate or accommodate the new information into their existing schemas (Piaget, 1973).

I would also aim to create videos where the problem was complex enough to allow for multiple methods and perspectives to add value to the process.  Kim & Hannafin’s (2011) suggest a model of problem solving through Identification, Exploration, Reconstruction, Presentation, and Reflection that fits well with this goal.

The structures above are important considerations, but the context/culture are also key to creating something effective.  The main challenge of creating a math or science media experience is creating a problem worth solving to the students.  Factors like relevance/meaning in the student’s life and safety/trust in the learning environment play an important role in making a question worth answering or not.

When Jasper was created, video production was not as accessible as it is today, and the creators did an admirable job trying to create adventures that were relevant and fit with a wide audience of learners.  Now that making a video is so much easier, I would move away from making trying to reach a large audience.  The technology available now can be leveraged to create problems tailored to the learners – to their personal context, experiences, and interests.

References

The Jasper Series as an Example of Anchored Instruction: Theory, Program Description, and Assessment Data. (1992). Educational Psychologist, 27(3), 291-315.

Kim, M.C. & Hannafin, M.J. (2011).  Scaffolding problem solving in technology-enhanced learning environments (TELEs): Bridging research and theory with practice Computers & Education Volume: 56   Issue: 2

Piaget, J. (1973). To Understand is to Invent: The Future of Education. New York: Grossman Publishers.

## Anchored Instruction & The Jasper Series

The Jasper series uses context-specific stories (“anchors”) to serve as a guide for problem solving.  Anchored instruction, in the Jasper series, uses interactive video clips stored on a videodisc and accompanying physical items (such as maps) to help students with problem solving by presenting to them a situation.  Anchored instruction and examples such as the Jasper series help to support learning by providing meaningful, real-world contexts to math concepts as well as a way to scaffold complex problem solving.  The authors note that Jasper provides generative learning; a way for students to regularly use their current understanding to connect and construct new knowledge.

As technology has improved vastly since Jasper’s invention, there are now ways to further enhance Jasper’s effectiveness.  For example, the amount of data that can be stored on a flash drive many times greater than that of the videodiscs the researchers used.  This would allow for many more or longer videos, providing opportunity to develop more engaging and deeper problems for students to view.  It would also be quite the experience for the students if anchored instruction were to take place in virtual reality.  This would allow students to explore the environment that the problem is situated in, perhaps looking for clues or manipulating objects to learn more about them.  In addition, the researchers noted that another benefit of the Jasper series was the embedded data in the problems themselves, and virtual reality would allow even more data to be shown when a student examines an object.

In particular, the object manipulation will be extremely useful in math learning.  Particularly in junior grades, many math concepts focus on objects and their characteristics such as surface area and volume which lends itself well to augmented or virtual reality manipulatives.  As they progress into senior math with more abstract concepts, dynamically changing graphs will allow students to alter equations and see, in real-time, the effects on the graph to better understand the patterns and relationships between values.

However, the Jasper method is not without fault.  Its narration still feels as if someone is reading a word question from a textbook, but overlaid on top of visuals.  Perhaps relaying the information (such as the plane’s fuel tank size) in dialogue between the characters in the video, as opposed to narrating it, may have it feel more natural.  Also, aside from its somewhat dated delivery method, one aspect that may be limiting is that the videos do not provide any feedback or ability to adapt to students’ progress.  For example, assessment of alternative solutions would have to be done by the teacher, but an expanded, interactive virtual reality environment may allow students to test solutions and self-assess their viability and validity.  But the concept of provide an interactive space to “anchor” student learning is one worth considering.

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(1), 65-80.

## Thinking Out Loud – A Conversation on Anchored Instruction

#### Alongside the writing on The Jasper Series by Cognition and Technology Group at Vanderbilt (1992) , Shyu’s (2000) research on implementing video-based anchored instruction in Taiwan, and Vye, Goldman, Voss, Hmelo and Williams’ (1997) research on middle school students and college students working through The Big Splash, are considered in the following response.

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Anchored instruction is based on the theories of situated learning, cognitive apprenticeship and cooperative learning with the aim to enhance student problem-solving skills (Shyu, 2000). Anchored instruction largely involves generative learning. CTGV (1992) describes generative learning, by quoting Resnick and Resnick, as necessary for effective learning. Concepts and principles “have to be called upon over and over again as ways to link, interpret, and explain new information” (p.67). Anchored instruction situates “the instruction in meaningful problem-solving contexts that allow one to simulate in the classroom some of the advantages of apprenticeship learning (CTGV, 1992, p.67).  As well, anchored instruction focuses on cooperative learning which allows for the construction of ‘communities of inquiry’ – a space for students to grow understanding through discussion, explaining, and reasoning or argumentation (CTGV, 1992; Vye et al., 1997).

In closing, Vye et al. (1997) mention other problem solving enrichments that have been established by others. Following is a collected list of further inquiry readings. These readings are referenced on p.479.

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), 1, pp.65-80.

Humphries, C. & Parker, R. (2015). Making number talks matter: Developing mathematical practices and deepening understanding, grades 4-10. United States of America: Stenhouse Publishers.

Parrish, S. (2014). Number talks: Helping Children Build Mental Math and Computation Strategies. Sausalito, California: Math Solutions.

Shyu, H.-Y. C. (2000). Using video-based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31: 57–69. doi:10.1111/1467-8535.00135

Vye, N., Goldman, S., Voss, J., Hmelo, C., Williams, S., & Cognition and Technology Group at Vanderbilt. (1997). Complex Mathematical Problem Solving by Individuals and Dyads. Cognition and Instruction, 15(4), 435-484. Retrieved from http://www.jstor.org/stable/3233775

## Anchored Learning and Jasper Woodbury

It has been my experience that although students may know how to solve a series of directed problems in mathematics given a formula or strategy, they have a difficult time taking that knowledge and applying it in a realistic situation. The Jasper Series attempts to move students beyond the basic component skills regularly taught in the classroom, to the higher level problem solving and generative thinking. In other words, students must learn to identify and define issues and problems on their own rather than simply respond to problems that others have posed for them (CTGV, 1992). The video series provide stories with embedded information needed to solve the problem the story poses. The information is often given within the dialogue, rather than explicitly with demonstrations, although this is also evident. This requires the students to analyze which information is important for them to use to solve the problem.

One of the positive aspects of this model is that the videos can be accessed by anyone, and most students will be able to glean information from the story, allowing all students to participate in the activity. There are many entry points for students at varying academic levels. Where some students are quite capable of thinking about Bernoulli’s principle and weight payload of the ultra-light, other students could easily measure the distance on a map. The beauty also lies in the affordance of the students to use their own strategies to come up with a solution, not an answer. There could be many solutions to the problem which takes away the notion of right and wrong, which allows students to take risks with their learning. Unlike other videos such as Khan Academy which are much more didactic in tone, telling the students what they need to know, rather than letting them discover it for themselves.

Although the Jasper videos are somewhat dated, the problems and solutions are still very relevant today. One thing that I thought might be interesting for older students to demonstrate their mathematics knowledge would be for them to create similar video scenarios, either for their peers or for younger students, following a similar format, and posing a challenge at the end. A project for the future perhaps.

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(1), 65-80.

Shyu, H.Y.C. (2000). Using video-based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69.

## Anchoring instruction (with PCK)

Dear class,

I am enjoying reading the posts and several extended conversations thus far analyzing the Anchored Instruction, Math Education, and Learning Disabilities literature. Anchored instruction continues to be used today not just in math but a number of different domains, including reading and special education. As you have already noted, it is an approach to teaching math that considers anchoring mathematics in situational problem-solving as key, and is yet different from other traditional and some contemporary resources and strategies available to us.

In response to the questions, a number of posts have been enhanced with analyses of anchored instruction, incorporating excerpts of problem-solving scenarios from the articles, findings from empirical research, and observations on video and digital technology included in the questions. Several of your posts thus far also have discussed the implications of teaching children or adults with or without learning issues (be they (mis)conceptions, learning disabilities, foundations in math, scaffolding learning, guidance and group processes, cognitive apprenticeship by older students, heuristics, visualization of a problem, “thinking out loud” to name a few) and cited the literature in some depth in this regard. Indeed, all of our teaching settings have students who require additional help.  There have also been several posts that have made connections to previous posts and a personal framing issues assignment.

Grounding anchored instruction with teaching examples from math (either specific to one of the Jasper videos from the situational video series) or particular math concepts or skills from your own context (eg. noting patterns, statistics, mathematical reasoning) has also been helpful in providing rich detail and begins to orient our discussions from PK towards PCK. I look forward to reading more of your thoughtful responses as the forum continues.

Thank you for all of your informed ideas on teaching math,

Samia

## Disengagement and Disconnection: Anchored Instruction as Active Involvement

The Jasper materials appear to be responding to issues of disengagement and disconnection. When student are not interested in their learning, they become disengaged, and disengagement can lead to reduced effort, reduced learning, and increased classroom management problems. When there is a perceived or actual disconnection between learning situations and the real world, between concepts, and between students and peers, it can be difficult for students to truly learn and understand a concept. Even the most well-intentioned teacher can miss the mark in creating “authentic” example scenarios for students. I agree with both of these problems. If educators want students to crave learning, students need to be able to recognize value and themselves in their learning experiences. While the Jasper materials are not a one-size-fits-all magic solution, they can definitely be a valuable component of a student-centered classroom and learning design.
The primary way in which the Jasper materials address these issues is through giving students an authentic purpose to their learning. The goal is not simply to complete a certain number of questions, memorize a particular formula, or use the right word at the right time. Instead, the goal with the Jasper materials is for students to connect with the story and decide on how it will be resolved. Students are in control of the path and the methods used, which allows them to find confidence in their own thinking processes, regardless of how they get to the destination. In their description of the application of anchored learning to high school statistics, Prado and Gravoso explain how although three student groups were not able to arrive at a correct answer, all groups applied the correct formula and values; the error was in computation. Anchored instruction tells students that their process is valuable, just as it is in a non-school situation. Even those groups who made a minor computational error likely showed increased problem solving skills and interest in statistics. Releasing some of the structure of the solution process can be challenging for teachers who are inclined to see the “correct” solution in a particular way. A pedagogical shift, however, to allow students to direct the process enables more engagement and more connection, both for the students and the teacher.
Contemporary videos available for math instruction seem to rest somewhere between a traditional classroom model of instruction and anchored instruction. While videos are becoming more and more interactive and open-ended, such as in embedded quizzes in some Khan Academy videos, the primary goal of most of these videos seems to be basic instruction. Although a video affords the viewer the ability to pause, fast forward, rewind, and access the instruction from any location at any time, ultimately, watching many of these videos is still a passive process. While these videos offer many classroom benefits such as being able to work with split grades, support students with different learning needs, help students stay caught up from home, and supporting a teacher when he/she is not confident in the material, the Jasper materials go further into collaboration and higher order thinking. The other videos can help ignite some interest among students and depending on the context, can help students better understand broad connections, but they are not nearly as effective as an experience that allows them to direct the process, that frames a narrative (kids like stories!), and that keeps them wondering and wanting to learn more.

Resources:

Cognition and Technology Group at Vanderbilt (1992a). The Jasper experiment: An exploration of issues in learning and instructional design. Educational Technology, Research and Development, 40(1), 65-80.

Prado, M. M., & Gravoso, R. S. (2011). Improving high school students’ statistical reasoning skills: A case of applying anchored instruction. Asia-Pacific Education Researcher (De La Salle University Manila), 20(1).

Shyu, H. Y. C. (2000). Using video‐based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69.

## The Jasper Series & Anchored Instruction

The theoretical framework underlying The Jasper Series is situated learning, in which knowledge is “contextually situated” and “influenced by the given activity” (Shyu, 2000). For the student, learning occurs through the use of generative activity and cooperative, social learning situations. Specifically, The Jasper Series utilizes anchored instruction which helps develop and apply “confidence, skills, and knowledge” a contextual, meaningful problem-solving activity (Cognition and Technology Group at Vanderbilt, 1992). Through this curricula, the classroom nurtures a student-centered lesson with the teacher encouraging students to develop skills and knowledge as a guide and not a dispenser of information.

Technology plays a role in enhancing the “emphasis on developing problem solving skills, communication, and reasoning” (Cognition and Technology Group at Vanderbilt, 1992). The Jasper Series is composed of seven features, one of which is utilizing a multimedia, video-based format that provides the basis for introducing the problem and following the lessons that follow and. These videos serve as the basis of a realistic story or context. In this scenario, technology is used as a motivating factor for students and aims to support complex understanding in the classroom. Further, the video supports reading, especially for students that may otherwise struggle with verbal instruction.

Personally, I have not heard of The Jasper Series prior to the videos and readings. The Jasper Series can be viewed as two distinct parts. One component is the strategy involving problem-based learning in the classroom. It’s clear from other experiments (Shyu, 2000 and Prado and Gravoso, 2011) that problem-based is an effective strategy to motivating and maximizing learning in the classroom. The second component from the series is the use of technology to initiate the problem. I wonder about the inclusion of technology and whether it is actually being used to its maximum potential. We use a very similar problem-based strategy at our school. Students are provided a problem and they have to solve through a series of processes and investigations. The primary difference, however, is that we don’t use a video clip to begin the problem; typically, we demonstrate or show students a problem. For example, in the Physics unit of Science 9, we demonstrate a complex circuit board (with light bulbs, resistors, etc.) that initially does not light up but does after several manipulations of the board. An extension that other teachers have used to this problem is having a model house and applying a similar circuit and students have to solve why certain bulbs do not function.   I would argue that, similar to the video, having a model or demo for students to examine also provides a real-world context for students. Ultimately, the question becomes how can technology be effectively used beyond enhancing the classroom and instead elevate the lesson?

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(1), 65-80.

Prado, M.M., & Gravoso, R.S. (2011). Improving high school students’ statistical reasoning skills: A case of applying anchored instruction. Asia-Pacific Education Research (De La Salle University Manila), 20(1).

Shyu, H.Y.C. (2000). Using video-based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69.

## My Love-Hate Relationship with the Jasper Series

At the onset, what’s not to love?  Two of the readings that I chose, concluded that students self-reported to enjoying math more, and having less anxiety (CTGV, 1992b; Shyu, 2000). Only one reading reported that students’ problem solving skills improved, but I would speculate that the one study that did not report an increase in this area, did so because the students only participated in one Jasper Series problem. Had the students in the Shyu study have a series of weeks immersed in Jasper, I suspect that their problem solving skills would increase in time.

The main issue that the folks at Jasper are attempting to address is that many students are unable to apply microcontext (“end of the chapter”) questions, to macrocontext (“real life”/situated/anchored) problems.  The literature that I read, convinced me of one thing—group work, when orchestrated well, is beneficial to most students.  In “Complex Mathematical Problem Solving by Individuals and Dyads”, the younger, Grade 5 dyads, performed much better than their older (and more mathematically talented) Grade 6 soloists (Vye, 1997). Two lesser-able heads and better than one more-abled, it seems. How great is that???

I am not convinced that diving head first into Jasper methodologies is wise, however.  The entire premise favours a “top to bottom” skills approach, where the focus is on higher level thinking, and to scaffold if and when needed.  In my experience, this is a disastrous methodology to follow to the tee when teaching mathematics.  In order for these higher level problems to be attacked, a base knowledge needs to exist. Otherwise, in the group work, one or two “hot shots” will take the lead, the students who don’t understand a stich, get pulled along, everyone advances to the next level, and sure… Everyone feels good, because the low level students had life jackets on the entire time—of course, they enjoy this approach!

Borrowing a thought from John-Steiner and Mahn’s 1996-piece, “Sociocultural Approaches to Learning and Development: A Vygtoskian Framework”, the authors emphasise the importance of when looking at Vygotskian Theory, to refrain from abstracting portions of the theory, which can consequently lead to “distorted understandings and applications” (p. 204).  To me, the Jasper folks have abstracted portions of constructivist learning strategies, conducted studies using the best math students or studies where groups can make the struggling kids float, and declared, “Hey, we’ve made math fun and relevant!”

Many of us agree that Piaget and Vygotsky had a lot of things right in their constructivist theories.  Both theorists agreed that the material world aids development due to environmental experience (Glassman, 1994). These environmental experiences are often transpiring amongst peer groups, in a social context. Can we not replicate these transformative experiences in our classrooms?

When students possess self-generated motivation to accomplish a task (due to being adequately challenged), constructivist approaches to learning can flourish (vonGlasersfeld, 1983). But here’s the thing… according to Vygotsky, the development of thought requires spontaneous (self-generative) concepts to occur in opposition of non-spontaneous concepts (Glassman, 1994).  Non-spontaneous concepts can occur through peer interactions, however, they can also occur through instruction, from adult MKOs (more knowledgeable others). Vygotsky himself was privately taught by a mathematician who followed the Socratic method. He learned an incredible amount from his parents and his tutor; his own children were brought up in a similar Socratic environment living in a single room house with 11 other people (please refer to the Vygotsky timeline: http://vygotsky2016.weebly.com/).

Ultimately, I would urge educators to digest methodologies like Jasper in small quantities.  These approaches are not the magic pill that will solve all of our problems. I believe that rote learning still has its place in mathematics. (Yup. I said it.) If it is the only approach that one adopts, I would ask that person to get with the program, however. We don’t want to kill the beauty of mathematics for our students, yet students moving onto academic levels of math, need to have the skill set, the automated skill set, in order to succeed and actually understand what the heck they are doing.

I’m still looking for that magic pill— it’s a quest worth pursuing, indeed! I suspect that if someone ever DOES find it though, that it will not consist of just one approach.

References:

Cognition and Technology Group at Vanderbilt (1992b). The Jasper series as an example of anchored instruction: Theory, program, description, and assessment data. Educational Psychologist, 27(3), 291-315.

Glassman, M. (1994). All things being equal: The two roads of Piaget and Vygotsky. Developmental Review, 14(2), 186-214. doi:10.1006/drev.1994.1008

John-Steiner, V., & Mahn, H. (1996). Sociocultural approaches to learning and development: A Vygotskian framework. Educational Psychologist, 31(3), 191.

Shyu, H. Y. C. (2000). Using video‐based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69.

Von Glasersfeld, E. (2008). Learning as a constructive activity. AntiMatters, 2(3), 33-49.
Available online: http://anti-matters.org/articles/73/public/73-66-1-PB.pdf

Vye, N. et al. (1997). Complex mathematical problem solving by individuals and dyads. Cognition and Instruction, 15(4), 435-450.