Monthly Archives: February 2017

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

PCK and TPACK in Module B

Dear class,

It was great to read how you are thinking about TPCK  in terms of your own practice. PCK and TPCK or TPACK will help to frame our discussions throughout Module B. A few “snapshots “of ideas and questions are collated  below. (You can search using the text to locate and read more about the teaching strategies used by our class members). As you are reading them, it will be useful to think about which strategies you would like to try? How would you modify them to support TPCK in your teaching context?

 

  • Jigsaw Research. Individually, students are each responsible for one part of the content knowledge.
  • Scientific Inquiry. Write out the steps to make an ice cream sunday.
  • Solar system. Students created models of our solar system not in the usual sense but rather to scale (obviously with in reason but they had to understand that and explain it). This activity required students to use math skills in measuring and finding replicas of the size of each planet in relation to each other. It involved problem-solving and collaboration ( I can’t tell you how many groups ended up frustrated when they chose thin thread to represent the distance- thin thread tangles easily and when it is metres long it is even harder to control). Students had to figure out how to store their projects so they didn’t return each day to a jumble of threads. In addition to their own amazement at the distance of the planets from each other and their size they also had to find a way to demonstrate this to students in grade one and two.
  • Digestive system. For example, for a science unit on the human body, my students and I explored, together as a class, the digestive system, which included some textbook reading (read and discussed together as a class, not individually), a look at x-rays of human intestines (belonging to a colleague of mine who recently retired and passed on a set of old x-rays to me – the kids love them!), student diagrams/models, and so on. Once we have done one body system together, students are sent out to research and become “experts” on one other body system that they will be able to share with their peers.
  • Sig. figs. significant figures to real world data. Following discussion of these topics, students then complete a mini lab where they use lab equipment (such as meter sticks, rulers, calipers, tape measures and various graduated cylinders) and apply those concepts to practical measurements. They are faced with four problems that involve measurement and calculations that will assist them later in the course.
  • Structures. One of my favorite science units to teach is Structures, Mechanisms, and Forces. During this unit the students build a variety of structures out of different materials, for different purposes, and make observations about the process. As a way to bring the unit together at the end we do a study of Rube Goldberg and his fantastic machines.
  • Fractions When I teach students about fractions, I spend time developing understandings with physical manipulatives (e.g. coloured cubes, fraction magnets, egg cartons and marbles, fraction pizzas) and digital simulations in Smart Notebook or on the iPad, and then move into the more abstract concepts of the written algebra.  This comes to mind as an example of PCK (or TPACK
  • Bridge building. My own personal experience with TPACK (although I did not think about it in such terms) came in a Science & Technology 11 course in which I did a unit on bridge building.  Throughout the design of the unit I went through the various stages that Shulman discussed, from comprehension (understanding trusses and force distribution), to transformation (planning lessons and designing activities), to instruction (lessons), and evaluation (assessing their final bridge projects).
  • Algebra. One strategy that I have only recently used, is to teach/review algebra with my FPC Math 10 (academic math) class, having the students sit in pairs of their choosing. Each pair has a table top whiteboard (London Drugs sometimes clears them out…), marker and eraser.  I review the basic “moves” and reinforce opposite operations and remind them that the order of the “moves” is important (“Reverse BEDMAS”, usually helps them remember).  Then, we do a series of increasingly difficult algebraic problems, WITHOUT variables. For example, rearrange “2 + 3= 5” for 3
  • Lunar phases and tides. I sent the students an excel file with data on the times when the ocean was at high tide and low tide. We had spent some times prior discussing the phases of the moon and the gravitational influence on the ocean water.  Then they investigated how the times changed different times of the year in different regions of the world. They choose a country and researched how the changing phases of the moon, seasons and orbit impacted that particular country certain times of the year.
  • Telling time. Digitally I use an interactive clock on the smart board to practice telling time, and I also have children engaged in time games which helps solidify understandings in a fun way.
  • Biology. Blood types and transfusions shows up in the biology 30s Manitoba curriculum under the circulatory system. The presence of antibodies is explained and the Blood Typing Came from Nobleprize.org (https://www.nobelprize.org/educational/medicine/bloodtypinggame/) is used to help gamify transfusions and help the development of the concept in an engaging way.  I suppose this is where I use technology and essentially  I am using TPACK at this point in the lesson.
  • Learning plans. One example of incorporating PCK in my own teaching is in constructing individualized student learning plans for each of my students. As a distance learning teacher, I work with each student individually rather than offering a standard course or program.  Throughout the year, the student learning plan evolves as necessary,

For several you, (re)reading Shulman helped to clarify ideas and raised new questions, such as: What sort of balance needs to exist between content and pedagogical knowledge? I was struck by quotes I hadn’t really even noticed before. For example, Shulman (1986) states: Teachers must not only be capable of defining for students the accepted truths in a domain. They must also be able to explain why a particular proposition is deemed warranted, why it is worth knowing, and how it relates to other propositions, both within the discipline and without, both in theory and in practice. TPCK is useful to think about as we engage with examples of TPCK in this module.

Thank you for your contributions towards this organizing framework,

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.

Transforming Teaching and Learning through PD – {a better late than never posting;)}

During Module A discussion, the need for educational technology related professional development for teachers was highlighted as necessary in equipping teachers for technology use in their classroom. The specifications of professional development were not thoroughly described in the discussions, which welcomes Mishra and Koehler’s (2006) detailed explanation of effective professional development using a “learning-technology-by-approach design” (p.1035). This approach incorporates TPCK and focuses “on learning by doing, and less so on overt lecturing and traditional teaching. Design is learned by becoming a practitioner, albeit for the duration of the course, not merely by learning about practice (Mishra & Koehler, 2006, p.1035). TPCK encourages professional development in an alternative process than is typical through workshops; professional development needs to be an integration of learning about the technology (content) and learning to use the technology in an authentic learning context (pedagogy). “Standard techniques of teacher professional development or faculty development, such as workshops or stand-alone technology courses, are based on the view that technology is self-contained and emphasize this divide between how and where skills are learned (e.g., workshops) and where they are to be applied (e.g., class- rooms)” (Mishra & Koehler, 2006, p. 31). Also key to TPCK, is the learning not of specific programs – software or hardware, but of the underlying principles of technology use. This is essential as “newer technologies often disrupt the status quo, requiring teachers to reconfigure not just their understanding of technology but of all three components [i.e. content, knowledge, pedagogy]” (Mishra & Koehler, 2016, p.1030). Developing a repertoire as described by Wasley, Hampel and Clark (1997) and quoted by Mishra and Koehler (2006) as ‘‘a variety of techniques, skills, and approaches in all dimensions of education that teachers have at their fingertips’’ (p. 45) helps to equip teachers to move from a professional development experience into their classrooms and choose the technology tools that will best meet the needs of their students. This supports Petrie’s (1986) extension of Schulman’s aphorism, “those who can, do; those who understand, teach” (Shulman, 1986b, p. 14) as he describes understanding as needing to be “linked to judgment and action, to the proper uses of understanding in the forg­ing of wise pedagogical decisions” (as quoted in Schulman, 1987, p.14).

The term “transformation” that Schulman (1987) uses to refer to the experience that occurs as content knowledge is passed from teacher to student provides an effective visual image. He describes this transformation as  “the capacity of a teacher to transform the content knowledge he or she possesses into forms that are pedagogically power­ful and yet adaptive to the variations in ability and background presented by the students (p.15). This transformation offers opportunity for individualized learning, teaching for the student rather than at the student, and aligns well with my teaching experience at present:

One example of incorporating PCK in my own teaching is in constructing individualized student learning plans for each of my students. As a distance learning teacher, I work with each student individually rather than offering a standard course or program. Conversations are held prior to the start of the learning year to design a student learning plan that consists of curriculum, resources, activities, etc. that cover the content area prescribed for the student’s grade level, but also adheres to the student’s interests, abilities, learning environment and effective ways of learning. Throughout the year, the student learning plan evolves as necessary, but again with the individual student’s needs guiding the changes. As students share their learning with me throughout the year, I provide specific feedback often suggesting areas that they can grow in their representation of ideas, as well as designing or recommending specific assignments to further their learning experiences. Although the forms of transformation may look different in a distance learning context, the process of moving from “personal comprehension to preparing for the comprehension of others” (Schulman, 1987, p.16) still occurs through preparation, representation, instructional selections, adaptations and tailoring. (Schulman, 1987).

 

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. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4 -14.

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

The tales of blood – PCK and TPACK

Shulman (1986) differentiates between content knowledge and pedagogical content knowledge (PCK).  It is true the teacher must be an expert in the content she wishes to teach but at the same time must also be an expert in how to teach that content.  This is where Shulman (1986) suggests PCK is, “…the most useful form of representation of those ideas, the most powerful analogies, illustrations, examples, explanations, and demonstrations…” (p. 9).  The ideas he speaks of are the content, the concepts, the specific learning outcomes outlined in the curriculum guides.  It is essentially not enough to know the stuff, but to know how to help students know that stuff that you know so well.

An example of PCK I have used in the past that has anecdotally worked well for me is the topic of blood types and blood transfusions, hence the title of this post :).

Blood types and transfusions shows up in the biology 30s Manitoba curriculum under the circulatory system.  It is a challenge for students to understand how we have 4 different blood types, and why getting certain red blood cells (RBCs) can be beneficial to a patient and why others can be catastrophic.  In order to help illustrate these ideas I have used the analogy of donuts. I did not come up with this analogy, simply found it online and borrowed it like any teachers with the best of intentions at heart.

Basically the analogy goes that RBCs are like donuts, some have A sprinkles, some have B sprinkles, some have A and B sprinkles and some have no sprinkles.  Sprinkles are analogous to antigens found poking out on the surface of these RBCs that help identify the type of they are either A, B, AB, or O.  The Rh sprinkle is tacked on after when students are comfortable with the A, B, AB, and O.

Then comes the challenging part of identifying correct versus wrong blood transfusions where students often get lost.  Here the presence of antibodies is explained and the Blood Typing Came from Nobleprize.org (https://www.nobelprize.org/educational/medicine/bloodtypinggame/) is used to help gamify transfusions and help the development of the concept in an engaging way.  I suppose this is where I use technology and essentially  I am using TPACK at this point in the lesson.

I enjoy teaching this lesson as I get to talk about donuts and the game is fun to play.

Thanks,

Vibhu

Shulman, Lee S. (1986). Those who understand: Knowledge growth in teaching.  Educational Researcher,  15,  2., pp. 4-14.

Blood Typing Game. (Nobleprize.org). Retrieved from: https://www.nobelprize.org/educational/medicine/bloodtypinggame/

Goodbye Rote, Hello Anchored Instruction

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

My Initial Reflections on the Jasper Series

Although this post does not directly answer one of the questions posed, it provides a space for discussion about the series and I look forward to your ideas and reflections. I have provided another post which more directly reflects the questions posed.

Before reading the article about Jasper anchored instruction, I explored the videos just to get a feel for what this series entailed.  I also wanted to get my initial impressions without having much background. The first thing that struck me was that they were posed as challenges, which I believe would be engaging to students. Then I noticed that they were real-life explorations and I reflected that they would foster rich discussion amongst students. These problems or “situations” would allow students to test out, hypothesize, work and rework as they problem solved. It would be messy but rewarding. They may require some facilitation along the way or a sounding board, but the problem solving would be student centered.

Some questions I had after watching the videos were:

  1. Would it be possible to have the students conduct some of these situations in real-life? (as an adjunct to the videos)
  2. What background in mathematical terminology would the students require?
  3. Could the students competently solve these problems without some prior math knowledge in the area of exploration (rate, capacity, range, temperature, etc.)
  4. What software or platform was used to create and share the videos?

After reflecting on the videos I read the essential article, ” The Jasper Experiment: An Exploration of Issues in Learning and Instructional Design Cognition and Technology”. I was happy to see that many of my reflections correlated with the article.

Within the situational videos basic skills are important, but students develop them in the context of meaningful problem posing and problem-solving activities rather than as isolated “targets” of instruction (Cognition and Technology Group at Vanderbilt (1992). Students must learn to identify and define issues and problems on their own rather than simply respond to problems that others have posed. I also found it interesting that the videos naturally encourage cooperative learning in which students have opportunities to discuss and explain which can assist in solidifying understanding. It is also interestingly noted that working in these cooperative groups allows the students to monitor one another and thus keep one another on track. This would definitely allow the teacher to take on a facilitation role more naturally.

The videos align with the goals of the NCTM as well. These include an emphasis on complex, open-ended problem solving, communication, and reasoning. In addition, connecting mathematics to other subjects and to the world outside the classroom is encouraged. The Jasper videos seem to fit the bill.

Within the article it explains that educators allow the students as much time and room to work on these problems without teacher interaction. Some may see this as foolhardy and may contest that certain skill sets need to be taught before complex problem solving can occur. The Jasper Experiment believes that engaging students in real-world problems that are inherently interesting and important helps students understand why it is important to learn various sub skills and when they are useful. The Jasper adventures are purposely created to reflect the complexity of real world problems.

Within the article it is also noted that Jasper developers are continuing to work with teachers in order to collect “scaffolding” or “guidance” information to include  with the videos. So although the goal of anchored instruction is situated in engaging, problem-rich environments that allow sustained exploration by students and teachers, some purposeful scaffolding and guidance can assist the problem solving process in some situations.

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

Mathematics Instruction for Students with Learning Disabilities-Jasper and Reflections on my Teaching Practice

The article, “Mathematics Instruction for Students with Learning Disabilities: A Meta-Analysis of Instructional Components”, helped me to further analyze the Jasper series and its goals. Within this study the researchers sorted the studies by major types of instructional variables. Their interest was in the detailed curriculum design and teaching practices that resulted in enhanced mathematics and they focussed on the essential attributes of effective practice. They went further and defined “explicit instruction”, which in previous research has shown positive effects in terms of increased understanding of mathematical skills for students with learning disabilities. The researchers broke it down into three components: (a) The teacher demonstrated a step-by-step plan (strategy) for solving the problem, (b) this step-by-step plan needed to be specific for a set of problems (as opposed to a general problem-solving heuristic strategy), and (c) students were asked to use the same procedure/steps demonstrated by the teacher to solve the problem (Gersten, Chard, Jayanthi, Baker, Morphy & Flojo, 2009). They also looked at the methods that exemplify a generic approach for solving a problem, student verbalizations of their mathematical reasoning, using visual representations while solving problems and range and sequence of examples. They further investigated providing ongoing formative assessment data and feedback to teachers on students’ mathematics performance, providing formative assessment data and feedback to students with LD on their mathematics performance and peer-assisted math instruction.

The results of the meta-analysis rendered some interesting data. Firstly, peer assisted learning did not provide much benefit, whereas being tutored by a well-trained older student or adult appears to help significantly (Gersten, et al., 2009). When assisting students with LD in my classroom, this finding is important, as I often pair my students with LD with their peers in order to provide more scaffolding or scaffolding when I am busy helping other students. I will need to rethink this approach.

In addition the two instructional components that provided significant benefits were teaching students to use heuristics (a process or method) to solve problems and explicit instruction (Gersten et al., 2009). When reflecting on these findings I still have some questions. I do teach my LD students a certain process or method to solving mathematical problems but I also don’t want to limit their strategies as we are being told to allow them to explore mathematical problems with a variety of strategies. Now that I think about this, perhaps students with LD do not benefit from a variety of strategies but are best served with a limited number of strategies to use, at least initially. In terms of explicit instruction, I do provide this to my students with LD, although they are also part of any open-ended problem solving that we do in class. I feel it is important to expose them to this type of mathematics as well, but perhaps they would be better served working on other math during this time. That being said, the researchers found that explicit instruction should not be the only form of instruction, so perhaps I should continue to expose the LD students to our open-ended problem solving discussions.

Further findings showed that the use of graphic presentations for illustrative purposes encourages students to think aloud and tends to be effective across disciplines (Gersten et al., 2009).  One caveat seems to be that students should be shown how to use visuals. Also, the visual diagrams resulted in bigger positive effects when visuals were part of a multicomponent approach to instruction.  I do use visuals as a big part of mathematics instruction in my grade 2 class. Students are encouraged to “show what they know” in a variety of ways and visuals is a big part of this. When they explain their thinking visuals provide a map for them to follow and also help them in recognizing errors in their thinking. Providing specific visuals for LD students and showing them explicitly how to use the visuals one the mathematics lesson is completed will be a further goal. They may require further scaffolding, and not just from a peer.

They also found that the sequence of examples is of importance when new skills are being taught, so scaffolding is critical for student success. Examples and problems should move from simple to increasing complexity (Gersten et al., 2009). When reflecting on my own teaching, I find that I do this naturally with all students, as it makes sense to me to move from simple to more complex problems. That being said, and reflecting on the Jasper series, perhaps introducing complex problems that students have to work through and problem solve through may be of more benefit.  The Jasper experiment believes that engaging students in real-world problems that are inherently interesting and important helps students understand why it is important to learn various sub skills and when they are useful. The Jasper adventures are purposely created to reflect the complexity of real world problems (Cognition and Technology Group at Vanderbilt, 1992).  As part of inquiry teaching (a method I use to teach some of the time in my classroom), I often introduce mathematical problems based on math explored in read-alouds. For example, when reading the book “Iron Man” we explored measurement as we explored how big we thought the Iron Man, the science fiction character in the story, would be compared to us as students. So in this way I attempt to introduce concepts that lead the students down possibly unexplored mathematical pathways and see what they can produce. I am left with the wondering: Do LD students benefit from this?

Importantly, the study showed that the process of encouraging students to verbalize their thinking or their strategies, or even the explicit strategies modeled by the teacher, was always effective (Gersten et al., 2009). In my teaching practice I often use verbal understandings to gain a better understanding of student understanding/misunderstanding and for ongoing assessment to move forward. I do this for all students, but particularly for students with LD.

It appears that teachers and students also benefit if the teachers are given specific guidance on addressing instructional needs or curricula so that they can immediately provide relevant instructional material to their student.  Teachers require support!!  This is an important point to discuss as educators are often expected to know what to do in all situations with a variety of different styles of learners, with a variety of curriculum and with a variety of learning abilities. As Schulman (1986) noted in his research, teacher training and the type of training provided needs to be revised to reflect both content and pedagogical knowledge.  The fact of the matter is that educators do not have all of these skills and cannot devote the amount of time required to meet the needs of all students. Teachers require the supports of special education teachers, administration, professional development, etc. in order to gain and implement these skills.  The research further disseminates this as the researchers recommend that providing specific instructional guidelines and curricular materials for teachers  and co-teachers or providing support services, peer tutors, cross-age tutors and/or adults providing extra support would be of direct benefit to students with LD (Gersten, et al., 2009).

Interestingly the researchers found at there seems to be no benefit in providing students with LD-specific feedback that is specifically linked to their goal attainment (Gersten et al., 2009). This seems to refute the feedback loop that we are encouraged to use as educators in order to help students to move forward in their learning. I will have to consider this when providing feedback to LD students. Perhaps spending more time on heuristics and explicit instruction and use of visuals would provide better scaffolding for their learning. I look forward to your thoughts on these points.

References

Cognition and Technology Group at Vanderbilt (1992). The jasper experiment: An exploration of issues in learning instructional design. Educational Technology Research and Development, 40(1). pp. 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.

Shulman, Lee S. (1986). Those who understand: Knowledge growth in teaching.  Educational Researcher, 15(2)., pp. 4-14.