Rote instruction? Anchored instruction? Behaviourist teaching vs constructivism? What is best for *Today’s*** learner? Why did I highlight today’s over the other pedagogical terms in the opening sentences? Because today’s learner is different from the students of past generations. Not only have they grown up in a digital world they are entering a work force that is different from previous generations. Since the industrial revolution, education and career preparation (for the most part) have been based on behaviourist pedagogy, using rote techniques to prepare students for well-defined jobs. Most high school graduates headed into factory assembly, retail or other careers such as teaching and nursing. Teachers and nurses also followed the same pedagogical ideals “do it this way, this is best, this is how it has always been done”. Follow the rules and you will be fine. **

Most educators today realize that our system of educating our students has not changed all that much from the one room school house. But, the world has changed by leaps and bounds. By continuing with rote instruction techniques and rewarding students for good behaviour we are not preparing them for a world that has changed while education stood still. The Japer materials are responding to the need to transform education in order to provide students with the skills required in today’s work force; problem solving, critical thinking, creativity and collaboration to name a few. The creators of the Jasper project realized that students needed to not just understand computation skills and how to plug numbers into a formula but how to apply those skills, when to apply them, why they worked and how to construct their knowledge so it made sense in their world. Students needed to see links between math and science and the real world. Their world!

I totally agree with the ideals of the Jasper program. I spent far too many years teaching the way things were always taught, looking out at a sea of bored, disengaged students who either played the game to get along or acted out because they could care less. A very troubling result of this is that more and more of my students lost their creativity, or school had killed it. When given assignments, they were interested in only one thing: how do I do this to get it done, and get a good enough grade. They wanted to be spoon fed step by step instructions because they had learned that is how you survive. You may die of boredom but you graduated. Conform, do it the way you were shown and sit quietly may have made for some easy to manage classrooms but what have we created? Generations of graduates who do not know how to think for themselves. Class upon class of kids who learned that talking in class was wrong and collaboration is like cheating. How do we expect them to function in a work force that now prizes these skills?

We need to move away from teaching isolated rote skills and begin to use other techniques such as anchored instruction. The Cognition & Technology Group at Vanderbilt (CTGV, 1990a) defined anchored” instruction as;

instruction is situated in engaging, problem-rich environments that allow sustained exploration by students and teachers. In the process, they come to understand why, when, and how to use various concepts and strategies (e.g., Brown, Collins, & Duguid, 1989; CTGV, 1990). The anchors create a “macrocontext” that provides a common ground for experts in various areas, as well as teachers and students from diverse backgrounds, to communicate in ways that build collective understanding (Bransford, Sherwood, Hasselbring, Kinzer, & Williams, 1990; CTGV, 1991a). Macrocontexts are also designed to facilitate experimentation by researchers who want to compare the effects of using them in conjunction with different types of teaching strategies (p. 65).

CTGV (1992a) created the Jasper Woodbury Problem Solving Series,” a set of specially designed video-based adventures that provide a motivating and realistic context for problem posing, problem solving, and reasoning. The series also allows students, teachers, and others to integrate knowledge from a variety of areas, such as mathematics, science, history, and literature (p. 65). Each problem in the video series begins by having students watch a problem story. (When first introduced to the video students do not know they will be solving a problem or what that problem may be). When the story is finished, various mini scenarios are presented. The scenarios begin more simply with using presented information (students have the opportunity to go back and rewatch all or portions of the video story at any time) to solve more basic problems. After the initial straight forward problems are addressed more abstract problems requiring more advanced math and science skills are introduced.

The study by Vye et Al. (1997) Complex mathematical problem solving by individuals and dyads looked at a group of first year college students and high functioning 6th grade math students. Both groups were introduced to a Jasper Woodley video problem (The Big Splash) and asked to complete the various sub problems individually. A second experiment used fifth grade dyads to solve the same problems. It must be noted that:

Solutions to Jasper problems involve multiple goals that have a hierarchical structure, numerous constraints, multiple-solution options, and multiple-solution paths. Some of the cognitive processes involved in solving Jasper problems include formulating the subproblems needed to solve the overall problem, organizing the subproblems into solution plans, coordinating relevant data with appropriate subproblems, distinguishing relevant from irrelevant data, formulating computational procedures to solve subproblems and the overall problem, and determining the feasibility of alternative plans. Traditional school environments produce students who are ill-prepared to solve problems requiring the coordinated use of such processes; presumably because of this, Jasper problems are difficult to solve (p. 438).

Researchers found that in experiment 1 individuals solving the trip-planning problems failed to consider multiple plans perhaps because students may have felt that, once they had a solution, they had met the requirement (p. 471). While the college students outperformed the sixth-grade high functioning math students on most subtests it is interesting to note that the grade five math dyads performed more like the college students and the dyads often looked at multiple solutions (something that did not readily occur in experiment 1). “The explanation for the similarities across fifth-grade and college students may be in the degree to which members of a dyad can monitor the solution process and keep in mind the constraints and search space relevant to the problem. Members of the dyad may fluidly adopt different roles in problem solving as they switch between being listener and speaker in the verbal interaction (p. 479).”

Vye et Al. (1997) study highlighted an important pedagogical technique, allowing students to work in groups. In the group setting students can benefit from the skills and knowledge others bring to the group. It seems to be an effective method of using Shulman’s (1990) Pedagogical Content Knowledge (PCK) outside of direct teaching. Students have the opportunity to share what they know and may be able to teach others how they understand it. I often find students find ingenious ways of helping others understand difficult problems. This group method also extends to Mishra and Koehler’s (2006) TPACK model. Including access to technology for all groups is an excellent way to share the knowledge of students in the class and the technology skills they may possess.

The research by Hasselbring et Al. (2005) concluded that anchored instruction in groups enabled students, even those with math difficulty “to transfer skills learned during instruction to a variety of problems. These findings indicate that a much more robust relationship between these students’ declarative, procedural, and conceptual knowledge was developed (np).”

In terms of technology that is available today (In what ways do contemporary videos available for math instruction and their support materials (c.f. Khan Academy, Crash Course, BBC Learn “Classroom Clips” and “Academic Earth”, video clips in Number Worlds, or others) address or not address these issues?) I think educators will easily find programs that use rote pedagogy to help students learn a skill. I also believe for many this is the only thing they look for, a game like interface that drills basic skill. I do believe there are valuable programs out there that are like the Jasper Woodley series but I believe they are far less used. Why? As mentioned in several of the ETEC 533 interviews: Time, accessibility and teacher understanding. Teachers do not have the time to learn these new programs with a confidence level needed to use it in a classroom situation. Access to technology is a huge problem in many schools (hardware, software and broadband issues). Teachers do not have the skill to troubleshoot problems and feel too much time is wasted in a class if technology crashes.

Personally, I believe many staff members feel overwhelmed by the possibilities and therefore it is easier to do what has always been accepted and done rather than take the chance to try something new (similar to our students wanting to know exactly how to proceed with a project so they don’t go off course). It is time we take chances and show our students it is ok to not do something right. That we don’t give up, we try again. That we collaborate and problem solve, that we practice critical thinking and looking for alternatives. As I have said before our students at every age are capable of amazing things if they are given the opportunity to demonstrate it. Programs based on anchored instruction like the Jasper Woodley series need to become the norm rather than the exception.

Reference:

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

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

Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2005). Technology-supported math instruction for students with disabilities: Two decades of research and development. Retrieved December, 12, 2013 from Google Scholar as a pdf.

Mishra, P., & Koehler, M. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. The Teachers College Record, 108(6), 1017-1054

Shulman, L.S. (1987). Knowledge and teaching. The foundations of a new reform. Harvard Educational Review, 57(1)1-23

Vye, Nancy J.; Goldman, Susan R.; Voss, James F.; Hmelo, Cindy; Williams, Susan (1997). Complex mathematical problem solving by individuals and dyads. Cognition and Instruction, 15(4), 435-450

Hi Catherine, I love your passion and enthusiasm— I can tell that I would love to be your colleague! I very much agree with much of what you are saying, but before you throw the rote-baby out with the bath water, I ask you to consider this. When it come to the neurology of math learning, it has been shown that repeated practice is necessary for the learning to make it into our LTM and to carve clear pathways to that knowledge (Zamarian, Ischebeck, & Delazer, 2009). Students in high school who do not have their times tables memorized, nearly always have math classes until Grade 11 that are more like life-sentences. They have high anxiety, do not attempt much of the practice, avoid asking questions typically and in general, loath coming to math class. I do not think that not having memorized times tables causes these things, rather, I think that failure to have this basic mathematical skill memorized, represents the tip of the math-phobic iceberg— it is more like a symptom, as opposed to the cause.

Also, consider the issues that Ontario is presently having. The province has moved away from rote-learning for the last few years and math results are completely tanking. Now, elementary teachers are being mandated to teach a minimum number of daily minutes on math instruction. http://www.theglobeandmail.com/news/national/half-of-ontarios-grade-6-students-fail-to-meet-provincial-math-standards/article31636338/

My ultimate point is that when adopting new strategies, I believe it is advisable to not let the pendulum sway to an extreme. So keep some rote learning on the basic skills— ones that are critical to continue in academic mathematics in high school and post-secondary. But then, adopt new strategies that also allow students to receive the socio-cultural, anchored learning affordances. Best of both worlds!

~Dana

***

Zamarian, L., Ischebeck, A., & Delazer, M. (2009). Neuroscience of learning arithmetic: Evidence from brain imaging studies. Neuroscience and Biobehavioral Reviews, 33(6), 909-925. doi:10.1016/j.neubiorev.2009.03.005

HI Dana,

Thanks for the in-depth reply, love it! First of all, I am a totally grey area girl, meaning never do I see the total benefit of one idea over the abandonment of another. Hopefully, I can clarify some of my thoughts without getting everyone (including me) more confused!

1. While I agree there is a place for rote instruction in our k-12 curriculum and agree with the neurology you point out my concern is that it can not be rote, rote, rote. (I think our paths seemed to diverge as I was talking about rote for every math and science subject matter not just computation- your points are super valid for students trying to retain basic computation skills). An example of what I consider rote outside of the computation skills would be: If I am teaching algebra to grade seven students. Where a+7= 10, b-3=4, 3x=12 or x/4=4 if a student is given three questions of each type and is correct and can explain to me how they arrived at their answer (using whatever process they used) should I then be assigning twenty questions of each type thinking I am reinforcing the concept? I don’t think I am. Many educators I work with think it is how it should be done. My thinking is if they got the three questions right would I not be better off to have them apply this knowledge to a problem, where they combine concepts and use critical thinking skills while collaborating?

2. While I believe rote for computation has its place I believe there is also a time to realize that the lack of computation skill may be holding a student back (yes kids who can’t do computation often hate math). As I stated in a previous thread my daughter hated math, had math anxiety and generally couldn’t wait for math to end (and this was in k-6). After some soul searching we just said enough, she sucks at computation but not allowing her to use a calculator is stopping her and us from understanding if she is bad at all math (unable to grasp concepts etc) or is it just the computation. In grade seven unless the skill being tested was rote recall of math computation skills (which she bombed) she used a calculator. It took the entire grade seven year but she got over her math phobia (it became a general dislike which over the grades 8-12 morphed into, hey math is kinda fun). LeeAnn is capable of advanced understanding of concepts and even though she is in university (and taking statistics etc) she counts on her fingers and stresses at any kind of mental math. In a safe environment (like at home or in the car or with her university room mates) she will play games to help her retain facts but she will never ever excel in this area. If we hadn’t had a grade seven teacher willing to go this route with us I know LeeAnn would dread and continue to have a math phobia and dropped it as soon as she could. We never would have known math concepts were actually a strength.

3. I appreciate your reference to the change in math requirements in Ontario but have to tell you my take on it. As I mentioned before I constantly frustrated by the bandwagon jumping in Ontario education. The concept of moving away from rote (at least in my district) was a memo saying don’t do rote have students solve problems. There was little to no direction for teachers and most had no idea how to instruct this way. I walked into countless classrooms during a math lesson where students were lost and floundering, only to hear the teacher say, “its problem solving, you have to figure it out yourself”. That is not instruction at all. Most have no idea what anchored instruction means. Many also totally abandoned any computation skills at all and direct instruction of any concept was avoided. (I think you may agree this was a recipe for disaster). Was it the educator’s fault? They were never trained? They did not understand the concept of non-rote instruction so they gave none at all. Even more frustrating for educators was they were mandated to move away from rote but the format of provincial exams didn’t really change to reflect this. It was a recipe for disaster and the disaster was inevitable. I always wonder why common sense seems to evaporate when educational changes are made. It is so frustrating.

I hope this helps clarify the issue I was attempting to make.

Catherine

Hi Catherine,

Wow— thank you for such an amazingly, thorough response! I have also found that the longer I teach, the more grey I become (not just on my head, haha!). Your daughter’s inspirational story perfectly exemplifies the mantra that to treat our students fairly, it does not mean that we treat them equally. Kudos to that Grade 7 teacher for recognizing her wall and providing her a route to circumvent her challenges. Soooo many bright students have IEPs that allow calculators for all math processes. The key is to have someone advocate for the student, as early as possible, so that the anxiety and dread can be minimized quickly. ~~~The thing about the amount of appropriate “rote”— I think that this amount is not set in stone for all learners. Personally, I give a minimal assignment in Math 10 (~10 questions per lesson), with 4 optional “further practice” questions, and 3 “challenge questions”. At the end of unit, I give two optional practice tests, as well. I am really emphasizing self-regulation of practice volume, since in 2 -3 years, they will be free birds in their post-secondary endeavors, having to completely self-regulate their practice. I always inform them that I was the type of math kid that would need to do ALL of the questions, in order to really get it down pat– I wasn’t the dullest or the sharpest knife in the box, for sure! ~~~How many times as educators has the government prescribed certain approaches and philosophies, without providing meaningful instruction as to how to implement? I really feel for teachers who did their best they could, yet only to find that the assessments did not reflect what the leaning outcomes said to pursue. I see BC going down a similar path with our move to Inquiry Learning and “Big Ideas”. There will be some folks who will be able to really rock this, but on the other hand, how many people truly understand the process of Inquiry? We have been given 2 or 3 days of “Curriculum Development” time, to wrap our heads around the new world order, but this time has not been spent learning how to properly run an inquiry learning environment. I’m concerned (and fairly confident) that the Globe and Mail will be running similar stories about BC Math, say in 4-5 years. ~Cheers, Dana the Grey

In my reading this week I came across a piece which describes 3 methods that teachers use to implement Jasper (and similar) problems(CTGV 1992a). In the first approach, teachers prioritize solving the problem the first time without errors. Rigorous prep on foundational skills is done to ensure students have master of the tools needed. In the second approach, students are taught the basics at a similar time to when they occur in problems. This minimizes frustration and but nudges the student into the teachers prefered method of solving the problem. In the third approach, the teacher provides scaffolding as needed. The student attacks the problem with whatever tools they have and may ask for help if they get real good and stuck.

I’m personally a fan of all three depending on the situation. There are some situations where mistakes are a major issue (medicine for example) where you need to get it right the first time. In most classroom situations though, I think students have to have a need for a cognitive tool before they will learn it. This would require teachers to have much more flexibility in how and when a concept is introduced but such an approach might just yield superior outcomes as students have a desire to use the concept instead of simply being required to.

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.

Hi Catherine,

I really appreciated your points on teaching to TODAY’S learner…not just utilizing the latest trend in teaching, but teaching to the students and their current environment. Your line about how many of us seemed to learn in school that “collaboration is like cheating” really stood out to me. Think for yourself was always promoted, which is a great thing to teach, but what if you do not know where to start? One thing I am learning, which has been challenging, is that the idea of remixing is not only ok but very powerful. One way I have encountered this was through learning about the Scratch coding community that actually encourages this “behaviour”. Letting go of the ropes and confined boxes is difficult but necessary.

When you were talking about the time constraints facing teachers to learn new programs and integrate pedagogy changing strategies, I think back to professional development issues. I totally agree with you that many educators seem to be overwhelmed by the vast amount of possibilities (and in elementary where teachers are typically generalists, focussing on only one subject can lead to neglecting others sometimes) and do feel that they may as well just keep doing what they have been doing or how things were taught to them because they “work”. I am often told, why reinvent the wheel? While this is definitely something to keep in mind in order to have some sense of time management in our teaching careers, it can also be negatively reinforcing the staleness of our profession as well. I find myself agreeing with Dana about similar problems most likely starting to pop up in BC in regards to our new curriculum…although we have been given extra “curriculum development” days, I find these days incredibly unstructured to the point of seeing many people spinning all over the place. While “professional autonomy” is important, direction and effective time management strategies are too. As I think I have mentioned before, it frustrates me to no end the amount of time we have been directed to learn about our new ancient reporting system to help us complete the same old traditional report cards, and then other opportunities to investigate new thinking, strategies, and programs seems to be on your own time. As Hickey, Moore, & Pellegrino (2001) discuss, why can’t we “[design] professional development programs that support teachers in understanding and adopting various curricular and instructional reform programs” (p. 649)?

Allison

Hickey, D.T., Moore, A. L. & Pellegrin, 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.