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.
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.
The thought that you shared about the efficacy of group work when “orchestrated well’ resonated with me. I think it is important for students to work in groups but I also think it is important that they be given strategies to work through problems that may occur when working in groups. I am sure we have all had the experience of working in a group that was not effective or in which one of the members did no work or in which some of the members could not problem solve well together. It can be frustrating and can stymie productivity. I wonder if conflict in group work ultimately changes the outcome when solving multi-layered problems like those posed in the Jasper Series? I also wonder about those students and learners who work best independently. I wonder if they just need more exposure to group work situations and if so would this increase their group problem solving skills? Or, would they continue to work alongside the group, but conduct their problem solving independently and just present to the group? Just some wonderings I have. Thanks for sharing!
Hi Michelle, Thank you for your comment. 🙂
I am not the best person to respond to your terrific questions, as I have relatively little experience having students learn cooperatively, beyond lab work. Since learning more about social learning and constructivist theory, I have been attempting to weave more peer interactions into my practice. This is where I am at…
1. The magic doesn’t just happen. It is important for students to feel comfortable with each other and know that they won’t be made to feel stupid.
2. You can put kids in groups, and without direct instructions, they will often sit together and just worked individually. What’s the point, right?
3. It is beneficial to break friends apart typically— I make exception to my highly anxious students, however. I think this is good because it keeps students more on task (less goofballing) and it provides opportunities for people to meet and work with new people— possibly even better people than had they chosen on their own.
4. I like to make the groups so that I can ensure that the talent is spread around the class.
5. Group work needs to include discussions of why the processes/steps are happening. Otherwise, the group work risks being simply a tutoring session that has students parrot the memorized steps. This needs a heap of teacher involvement, I have found. So I always circulate, and poke my nose into everyone’s work. I also will give shout outs to individuals who are really explaining things well, so that other people, who are brave enough, can go tap into the MKOs brain, too.
This is only my third semester of actively trying to collaboratively learn, but it is coming along. I do not do it for every lesson— but with a few years under my belt, what I do know, is what students don’t typically know. I am using this approach on those really tricky lessons, that need some extra care and attention.
I would love to hear from other folks about their group work strategies, too! I have a feeling, that it is a process that is as much of an art as a science.
Great post. As it pertains to math (and science) , I totally agree with you that group work can be beneficial – when the groups are carefully constructed and organized. Depending on the activity itself, I’ve prepared groups that are heterogenous and homogenous in skills and knowledge. The heterogenous groups do end up being led by a “hot shot.” To counter this, I’ve had students complete an accountability assessment following the activity to ensure that all group members are involved and responsible for their learning. It helps, somewhat. The homogenous group activities allow me to help the weaker students with the activity while the advanced skills can work independently.
In regards to the Jasper Series and its methodologies, I too am cautious as to how I would utilize it in the class. I could definitely use some aspects of the approach, especially when introducing a topic/concept and allowing students to run a little wild with their thoughts and ideas. As you mention though, I’d be a little more hesitant to use the series solely as a method of teaching a core concept.
Thanks for the post!
Hi Darren, Thank you for your comments! Truth be told, I have never tried homogeneous groups. Now that you have “planted the seed”, however, I can see how that would be advantage in some circumstances. I will definitely consider different combos, going forward. In the spirit of keeping friends together, I really like using table top white boards with partners, then sending students to assist other students, as the answers are being revealed. A nice thing about this is that sometimes students will switch roles— it’s nice to see someone giving help for the first time! 🙂 ~Dana
I certainly agree that there seems to be an absence of the struggling or unengaged student from the readins I did. I think these may have been discussed in some of the others though, perhaps someone can chime in on this? My understanding is that the Jasper Series aims, in part, to remove some of the barriers that prevent kids from getting at the problem as a relatable entity. The use of video instead of text helps to enable poorer readers and the searchability of the video allows students who need more time with this media to review it.
It certainly won’t solve all problems and I do think that our “keener” kids will probably get the most out of this sort of approach (if it is well managed), but I think there are certainly some useful design features that could really help to enable students who struggle with traditional “word problem” style questions.
All that said, students still have word problems and rote skills tests to contend with in the form of PAT exams and diploma exams here in Alberta. Choosing to use a Jasper style approach may have severe impacts on the, unfortunately, neccessary test taking skill that student in Alberta much master in order to get in to post secondary institutions (which themselves often operate on the same principles). It seems like there would need to be some serious top-down impetus for such an approach to be feasibly adopted.
Hi Daniel, Thanks for your reply! As I was digesting the concepts for Jasper, I felt that my gifted class would really enjoy digging into a multi-step problem. A battle of the wits, with teams and glory! Beyond doing something like this, I fairly certain that Jasper will not make its way into my lessons. Never say never, I suppose. If I thought more about updating the concept and utilizing it in combination with other strategies, who knows… ~~~ The assessment issues can’t be ignored, as you have pointed out. Did you catch today’s Current? It focused on abandoning letter grades. My Principal has mentioned on more than one occasion that she is in favour of abandoning final exams. Things are changing, but I do not know if it is for the better! ~Dana
I certainly agree with your sentiment on balance in mathematics, particularly that students need to have a good grounding in the basics before they can begin to process the thinking required for those higher level problems. If there is no grounding in the basics the students will be spending too much time trying to figure out how to convert measurements, or distances without being able to see passed that to solving the bigger problems. I am a huge proponent of balanced math, meaning that there is a place for extra practice of basic math facts such as multiplication tables, as well as the higher order thinking problem solving that is required in the real world. I would use these video series in my classroom but I would want to be sure that my students had all the resources and understanding of the basic math principles as well.
Hi Anne, You and I are cut from the same math fabric! 🙂 The one time, as a student in grade school, that I dreaded math, was when I clearly did not have the basic skills down pat. I was at the end of my Grade 3 and I was at my third school in that grade. I was so behind the other kids with my times table knowledge. I would feel so dumb because we would sit in groups of three with a student flashing cards and testing us. Public humiliation felt horrible! However, once I caught up in that area, I started liking math again, and really appreciated the fact that with extra effort, I could do as well as anyone. When in Grade 5, Mrs. Wong gave us a challenge to complete all of the questions in the supplemental math text, I took her up on the challenge and was the first student done (and got the first pick off of the prize table!) You could imagine that my basic, fundamental skills were automated and accurate after having completed hundreds of extra questions. I truly believe that Mrs. Wong’s competition is one of two main reasons that I went on in math in university. It allowed me to confidently attack the more difficult problems in every math class in Grade School and set me up to enjoy learning new mathematics. I appreciate that not everyone will respond to rote learning competitions, as I did. But at the end of the day, it really worked for me. Ultimately, getting back to your comments, a mixed methods approach to math is my preferred route, too! ~Dana
Do you want me to be incredibly nerdy and share a quotation from the Shyu (2000) article that actually states that problem-solving skills did increase through the study completed with students in Taiwan? Yes??? This quotation may revert you back to a love-relationship. 😉
“In summary, the finding suggested that anchored instruction provided a more motivating environment that enhanced students’ problem-solving skills. Results also indicated that all the students benefited from anchored instruction through its effects on their problem-solving skills regardless of their mathematical and science abilities (p.66).
Hi Jessica, Embracing your inner-nerd, is always a good way to go in my books! Thanks for pointing this out— I went back and checked my notes, then checked the reading. I think where I became confused was when I read that “…there was no significant difference among ability-groups on their increment of problem-solving skills.” (p. 67) I interpreted that statement incorrectly! So, in truth, what the study found was that all ability levels demonstrated high problem solving skills, the increases between ability levels were statistically the same. Which is very different from my original interpretation! 🙂 Cheers, Dana
Jasper also offers, due to the longevity of the project, professional development on AI for teachers. Their pro-d addresses important questions like, when, how, and whom. (All of the projects in this module have had substantive engagements with pro-d which makes them great to explore in part for their outreach efforts).
Hi Samia, Could you direct me to more current information on the Jasper Series? I am still very skeptical about it’s place “on the main stage”, in an academic math environment. That is not to say that it does not have a place at all, but rather in conjunction with other methodologies. Alternative approaches to teaching are working for some schools; for example, the folks at High Tech High seem to be turning traditional classrooms on their heads. But even at High Tech High, where inquiry reigns, they do not use their model of learning in mathematics*. (*Told to me from my Superintendent, who toured HTH in recent years.) According to my Superintendent, HTH tried for many years to deliver mathematics in an inquiry, problem-based learning format, only to realize that their students were not adequately prepared for post-secondary. HTH has since returned to a more traditional, math approach. I wish I had evidence to provide that was not anecdotal! ~Dana
Hi Everyone, I have been doing math in partners or groups for about 7 years now. I have to say the approach changes depending on the group. Students, of course, start out working with their “friends” but I have found every single time students gravitate toward those who think like they do. They also quickly become aware of who is a liability (just want to tag along and have others do the work), some students ( usually those who are the math whizzes) ask to work independently. For the most part, they slowly gravitate to groups as the year progresses. If they do not we usually talk about why. The students in my class are welcome to work on their passion projects when they finish other class work and this is sometimes the motivator to work independently. Many, though, after a breaking in period will ask if they can go help a group that may need assistance. The hardest part for me as a teacher is letting the first two months just happen. I found if I interfered with groups too much it was detrimental. I am always circulating or at the “help desk”- individual students will come to represent their group and ask questions. Some groups form around or close to the “help desk” usually those groups who may struggle. Assessment also happens often, at any time and students know this. When I stop by a group they know that anyone in the group can be asked and are expected to defend their solutions. No one wants to be in a situation where they have no idea what is going on. While I never beat a student down for not knowing, it usually leads to a discussion on group dynamics and being accountable to themselves for their learning. It is a dynamic complex system, and it took me a really long time to not interfere with it. (Of course, that is not to say intervention is never necessary, sometimes groups need redirection) all part of the education process. As is, in my opinon the need for direct teaching of some skills.
There is no black or white in education it is all different shades of grey.
Hi Catherine, Thank you for sharing your group work experience with us. Knowing when to intervene and when not to, is a tricky one, for sure. I have to go out on a limb at times, but my preference is to act according to who is in front of me. I think the most important lesson that I have learned over the years is that students who truly struggle, rarely struggle because they “are lazy”. (Bring on the grey area!!!) There can be so many external factors at play when a student appears to simply not be trying. As someone who is relatively new to group learning, my gut is telling me to intervene more on the front end of the course, then to hang back as groups of students can work independently. Another consideration that I should be mindful of is that I have about 1/3 of my math class right now from other countries (where the math skills tend to be more advanced than in Canada). I tried making my groups up that split my International students up last week— it seemed to work well for both language and mathematical benefits! ~Dana