Author Archives: Derek Cowan

Super Math World and youcubed

I have been using Super Math World ( in my grade 5 class for the last two years. It is a great example of immersive game-based learning for younger learners. I first came across it when exploring and Jo Boaler, which is an amazing website. I use it for problem-based whole group lessons, as well as with small groups to reinforce specific concepts. I have kids use small white boards to solve problems symbolically and then test their thinking in the games 3D environment.

Image result for supermath world

T-GEM, PhET and Friction

Understanding the effects of friction on the motion of objects can be a difficult concept for some students to understand. To explore the topic further, I designed a blended lesson using the T-GEM model and a PhET simulation, along with two others. The de Jong and van Joolingen (1998) review of simulation use in discovery learning contexts cited the importance of structuring and supporting students’ work in ways to prevent difficulties (Stephens, 2014). The teacher will lead some aspects of the lesson but students will be active participants throughout. Small groups will record observations and responses on this collaborative document which will help guide and structure the experience.


Prior knowledge accounts for the largest amount of variance when predicting the likelihood of success with learning new material (Srinivasan, 2006). Therefore, it is essential to activate relevant prior knowledge. Students will discuss and analyze scenarios where friction is the cause of their observations. Two common ones at my school would be tobogganing on the hill and hitting a patch of grass or participating in Halloween gym and having to scooter over a long stretch of carpet. Students will also play a game emulator of Mario Kart ( and drive over different surfaces and use different characters to observe the impact that their characteristics have on the motion of the vehicles. Students will explore a simple BBC simulation ( in which they can test the effects of different surfaces on the motion of a vehicle using the same applied force. Students will record observations on the recording sheet and generate ideas regarding the relationship between friction and motion.

Students will then engage with a more detailed PhET simulation at They will freely engage with the simulation but also use information on the recording sheet to test specific scenarios to observe and compare the interaction of multiple variables in more detail.


Students will engage in a whole class lesson using the simulation. The teacher will highlight crucial concepts, spend time addressing conceptual difficulties, focus on key visual features of the simulation (frictional force), and promote students using key visual feature in their thinking (Stephens, 2015). Students will evaluate their generated ideas relative to their whole group experience.


Students will go back and use the simulations again. They will reread answers on the recording sheet as well. They will have the opportunity to revise and update their groups initial responses to reflect a new more comprehensive understanding.

Using a variety of objects, surfaces, and spring scales, students will create a real-life scenario that demonstrates the effect of friction on the movement of objects based on the simulations they used.


Srinivasan, S., Perez, L. C., Palmer, R., Brooks, D., Wilson, K., & Fowler, D. (2006). Reality versus simulation. Journal of Science Education and Technology. 15(2), 137-141.

Stephens, A. L. (08/2015). Computers and education: Use of physics simulations in whole class and small group settings: Comparative case studies Pergamon Press. doi:10.1016/j.compedu.2015.02.014


The many quality digital resources were very engaging to explore this week. By connecting student learning to real-world authentic learning environments these networked communities increase engagement and make learning purposeful.

Depending on how educators structure learning, I tend to agree that Globe represents an example of Anchored Instruction. Provided that students actively engage the experience through open-ended problem-solving with the goal of constructing assessible knowledge that can be applied when required.

According to the Cognition and Technology Group at Vanderbilt, Anchored Instruction is “situated in engaging, problem rich environments that allow sustained exploration by students and teachers” (1992a). Its design immerses students in “meaningful problems for students to solve that capture the intricacies of real-world mathematical problem solving” (Vye et al., 1997). Students experience problems as practitioners in real-life contexts encounter them. They work collaboratively with peers and socially construct knowledge through experience and argumentation. An anchored instruction “activity supports learning opportunities that relate to and extend thinking to other content areas” (Fried, 2005).

GLOBE anchors instruction within the real-world scientific data represented on the website and even involves students in the collection of data for use in actual scientific studies. GLOBE is organized into several separate “investigations,” each focused on a different aspect of the environment (Howland, 2002). The networked community goes beyond the capabilities of the Jasper Project, but both provide an engaging digital context for students to explore through independent investigations and open-ended problem-solving. It facilitates the creation of a shared experience for learners which is then utilized for deeper knowledge construction. Students learn within wide collaborative communities, including Globe scientists, and engage interdisciplinary issues “not just as learners but as scientists themselves” (Penuel, 2004). It facilitates clear connections between math and science topics. Unlike the Japer Series, GLOBE does not contain as an explicit “story, adventure, or situation that includes a problem or issue to be resolved and that is of interest to the students” (Fried, 2005). However, I believe that the experience itself could be framed in a similar way.

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.

Fried, A., Zannini, K., Wheeler, D., Lee, Y., & Cortez, a. J. (2005). Theory Name: Anchored Instruction. Retrieved from Suny Cortland:

Howland and Becker (2002). GLOBE: The Science behind Launching an International Environmental Education Program. Journal of Science Education and Technology, Vol. 11, No. 3 (Sep., 2002), pp. 199-210

Penuel, W.R., & Means, B. (2004). Implementation variation and fidelity in an inquiry science program: Analysis of GLOBE data reporting patterns. Journal of Research in Science Teaching, 41(3), 294-315.

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.

Embodied Learning

All of the papers I read related in that they connect knowledge construction to actions and movements within learning environments.

Winn (2003) argues that the recent focus of educational research on constructivism has ignored some aspects of learning and advocates a return to a more computational view of learning. He considers of how our “physical bodies serve to externalize the activities of our physical brains in order to connect cognitive activity to the environment.” (p. 88) In his view, “learning is considered to arise from reciprocal interactions between external, embodied, activity and internal, cerebral, activity, the whole being embedded in the environment in which it occurs” (Winn, 2003).  He discusses how technologies can create artificial environments that to bring students to concepts that lie outside the reach of direct experience.

Zhang et al. (2010) discuss developing a mobilized science curriculum to help students “become self-directed and social learners who could learn everywhere and all the time using mobile technologies.” (p.62) The researchers advocate using mobile technology to connect with a broader range of learning environments. The mobile technology allows the students to be more active and bring the technology to the relevant aspects of the environment.

In a 2014 study From Action to Abstraction: Using the Hands to Learn Math researchers found that students learning abstract gesturing connected to math was an effective learning strategy. It was compared with students physically acting on their environment and a concrete gesture miming an action. While all three were found to be beneficial “only gesture led to success on problems that required generalizing the knowledge gained” (Novak et al., 2014). The researchers suggested that gesturing while saying words may help learners process the words associated with the learning in a less superficial way.

Connecting movement to learning concepts is something that I am constantly trying to find ways to accomplish. I have been using a game called Super Math World ( formerly Mathbreakers) to teach number concepts. It’s a little hard to explain but students are immersed within a 3D world and interact with their environment to create specific numbers by combining, dividing, multiplying, etc. in order to progress beyond barriers and enemies marked with a value by “zeroing” them out. This year I brought them to the gym where they had to design their own “level” based on the design of the game. They had to consider the relationships between numbers they included, the required operations and ensure that there were multiple solutions to the level. Its is a challenging game but the movement and actions incorporated brought the problem solving to a whole new level. They came back with a deeper understanding which generalized back to the digital game.

In another course, a student introduced Smallab Learning which is  designed around embodied learning. It looks very interesting…


How can we purposefully include gesturing in mathematics instruction?

Does anyone include role play activities in math and science?

What are some examples of reasonably accessible technologies that support embodied learning?


Ahmed, S., & Parsons, D. (2013). Abductive science inquiry using mobile devices in the classroom. Computers & Education, 63, 62-72.

Novack, M. A., Congdon, E. L., Hemani-Lopez, N., & Goldin-Meadow, S. (2014). From action to abstraction: Using the hands to learn math. Psychological Science, 25(4), 903-910.

Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation.  Technology, Instruction, Cognition and Learning, 1(1), 87-114.

Design Project and LfU

Edelson (2001) proposes the Learning-for-Use model (LfU) which is a design framework that promotes student’s construction of “deep, interconnected content knowledge and inquiry skills through activities that incorporate authentic scientific inquiry” (p.365). Based on learning principles shared with constructivism and situated learning theory, its goal is to “overcome the inert knowledge problem by describing how learning activities can foster useful conceptual understanding that will be available to the learner when it is relevant” (Edelson, 2001). Student learning is guided by a process involving motivation, knowledge construction and knowledge refinement.

While reading the Edelson article, I reflected on how a design project I typically teach could be redesigned using the LfU learning principles and steps. During the project, students design and build vehicles in engineering teams to accomplish co-constructed goals. We investigate math and scientific concepts related to the design and performance of the vehicle. My grade team typically had a representative from a robotics design competition come in. However, the content was taught didactically through lectures and focussed on memorizing content. Like the article explains “the focus on memorization leads to “inert knowledge” that cannot be called upon when it is useful” (Edelson, 2001). Students were not able to apply the knowledge when provided the opportunity. We changed the instruction a few years ago but the LfU design could further improve the experience.


By creating design challenges that are just beyond the current ability of the students to accomplish it “creates a desire (motivation) to address the limitation by acquiring new knowledge, and it creates a context in memory for integrating new knowledge” (Edelson, 2001). The challenge could be to increase the speed of the vehicle by improving handling or to design the vehicle to move a specified load. The basic design of the vehicle they build is not effective at engaging in either task.  Like in the Jasper Series, new information becomes a useful tool as opposed to an isolated fact.

Knowledge Construction

As students begin the design process they will construct mathematical and scientific knowledge relevant to the goals they are attempting to achieve. Working in small groups, students investigate the relationship between distance, time, and speed. They use digital scales and a variety of materials to experiment and determine the effect of weight and friction on the speed and control of the vehicle. When designing attachments to help move the load, students consider various likely scenarios and adjust their use of materials accordingly. They record their observations and explanations using OneNote and can revisit them after. The teacher role during this stage is to highlight relevant experiences, encourage reflection and facilitate collaboration between students.

Knowledge Refinement

During this step, the design goals can be connected. The students must design their vehicles balancing a variety of considerations. The goal we used this year was students had to complete against another robot to move a load out of a designated area. It was a combination of earlier goals and required the students to design vehicles with the speed, control, and materials necessary to effectively accomplish the task. Students must articulate their understanding of math and science concepts and explain how their designs take them into consideration. Knowledge is “reorganized, connected to other knowledge, and reinforced to support its future retrieval and use” (Edelson, 2001).

A variety of hardware and software tools can be integrated throughout the experience.

  • Google Sketchup can be used to design vehicle before using physical materials.
  • Explain Everything can be used to articulate conceptions and revisit them later. It also helps them present their thinking to other students.
  • Excel Online can be used to record data and collaboratively investigate relationships.
  • OneNote can allow students to keep a record of their experiences related to their designs.
  • Video can be used to analyze the movement of the vehicle and accurately determine its speed.


Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385.

What Impacts Global Climate Change?

I decided to explore the ‘What Impacts Global Climate Change” WISE project. The lesson is designed for grade 6-8 students and requires 4 – 5 hours. It explores how human actions affect global climate change. The lesson is carefully designed and constantly requires students to revisit and update their understanding. It provides continual descriptive feedback to learners and gives them multiple attempts to adapt their thinking. It was something that I thought I would be able to adapt for a slightly younger audience. It is also something that I know a lot of my students typically have some prior knowledge about but also a lot of misconceptions. Students “bring to science class multiple conflicting views of scientific phenomena, often tied to specific contexts, examples, experiences, or situations” (Linn, Clark, & Slotta, 2003). I began by trying to make the lesson more connected to the prior knowledge of my learners. A portion of the lesson was about how local changes can represent evidence of climate change. The project used information about Bengal Tigers. I chose to replace the topic of this portion of the lesson to the changes happening to the habitats of polar bears and northern communities. I thought that students in my setting would be able to connect with the issue in a deeper way with these topics, as they are familiar topics of study.  Designing “contexts for problems that connect to students’ personal concerns can motivate students to reconsider and revisit their ideas long after science class is over” (Linn, Clark, & Slotta, 2003). I added a link to a WWF Polar Bear tracker to see the movements of bears in Churchill, Manitoba. Students can choose animals to follow and see how scientists monitor bears and collect information about how changes are affecting their habitat and well being. I also added a video about local changes changing habitats and local communities.

I also noticed that many of the responses students were required to give throughout the lesson were done through writing. I wanted to make the project more accessible for a wider range of learners so added a draw step into the “How does the Sun warm Earth” section. This would allow students to represent their thinking through drawing instead of text. It allows them to create multiple frames and create a short movie clearly demonstrating steps in a process. I also embedded several flash games that connected to sections regarding how human actions affect climate change to create a more interdisciplinary investigation. I found a flash game that allows the player to offset emissions by making positive changes. I would connect this to the concept of a carbon tax which is a common current topic in the media. This could serve as an extension research activity that students can engage in with less support. It is “essential to assess the ongoing state of students’ knowledge in order to bridge their capacity to inquire and to fade support as students learn to accomplish their problem-solving goals without scaffolds” (Kim, & Hannafin, 2011).

Kim, M. C., & Hannafin, M. J. (2011). Scaffolding problem solving in technology-enhanced learning environments (TELEs): Bridging research and theory with practice. Computers & Education56(2), 403-417.

Linn, M. C., Clark, D., & Slotta, J. D. (2003). WISE design for knowledge integration. Science Education, 87(4), 517-538. doi:10.1002/sce.10086

Real-World Problem Solving

The Jasper Series is a technology-enhanced learning project based on Anchored Instruction. In which instruction is “situated in engaging, problem-rich environments that allow sustained exploration by students and teachers.” The designers were responding to research indicating that students “do extremely poorly when faced with situations that require them to generate the relevant subproblems and figure out what data are needed to satisfy the subgoals that they generate on their own” (Cognition and Technology Group at Vanderbilt, 1992a). While students can calculate numbers in isolated situations, they are relatively weaker at understanding how to apply these abilities within problem-solving contexts. The series of videos provides a guiding framework and presents “meaningful problems for students to solve that capture the intricacies of real-world mathematical problem solving” (Vye et al., 1997). Students explore information in interdisciplinary contexts, generate solutions collaboratively and critically reflect on their existing conceptions. This approach significantly differs from traditional direct instruction methods and recognizes “that the course of learning is not a simple process of accretion, but involves progressive consideration of alternative perspectives and the resolution of anomalies” (Confrey, 1990).

I think that many of the current video-based supports that exist for math are essentially virtual lectures and typically focus on procedural understanding. Many Khan Academy lessons demonstrate how to carry out calculations using a variety of operations and algorithms. One website that uses video in a somewhat similar way to the Jasper Series is called When Math Happens – 3 Act Math ( Like the Jasper Series, students generate an understanding of the sub-problems and the relevant information collaboratively. In each problem, three short video clips provide a real-world engaging context and helps to guide student thinking. The first video provides a visual context for a real-word problem. The second video scaffolds students’ generation of knowledge about sub-problems which they will need to solve the larger problem. The last video provides feedback for the student so they can evaluate their solutions. Some problems provide a “sequel” so students can extend their thinking. The technology serves to create a context which guides, motivates, and provides feedback for students. Student can repeatedly explore the videos for relevant information and visual clues help support their decisions regarding how to use the information.

Anchored Instruction connects to my understanding of Problem-based Learning. This year my class started a school snack cart to raise money to purchase technology. The math required to run the store provided content for PBL instruction in class. The kids had to figure out how to balance inventory, calculate profit margins, make decisions about which products to buy, etc.  We used Excel Online to work with the secretaries to manage the account. They used iPads to compare prices, record sales, evaluate nutritional information, etc. One thing I have come to understand while teaching with a PBL design is the significant PCK required to differentiate the experience for all learners when engaging in real-world explorations. The experience was great for many students, but it became complex very quickly. Some kids became lost due to “the intricacies of real-world mathematical problem solving” (Vye et al., 1997). Inclusion of all students depended on the anticipation of the math concepts that arise throughout the experience. I found this significantly more difficult than when I was selecting the content to introduce. Technology definitely helps, in this case digital pictures and video, because the students can access the problem through visuals instead of text. It also supported by reducing demands on memory. Many kids would take pictures of objects relevant to the problem and, through apps like Explain Everything, connect their mathematical thinking to the pictures.   

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. Retrieved from

Confrey, J. (1990). A review of the research on student conceptions in mathematics, science, and programming. Review of research in education, 16, 3-56.

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.

Minecraft TPCK

Shulman (1986) highlights why teacher assessments should move beyond evaluations of content knowledge related to subject areas. He argues for the importance of Pedagogical Content Knowledge (PCK) which “represents the blending of content and pedagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction” (Shulman, 1987). PCK refers to practices and decision-making regarding how to teach particular content. He argues that our understanding of teaching knowledge should include the capacity ‘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” (Shulman, 1987). Mishra, P., & Koehler, M. (2006) introduce the concept of TPCK, in which knowledge of the how technology connects to PCK. I think the conception of teachers as deliverers of content is still somewhat prevalent. The TPCK concepts provide a valuable framework to develop a more comprehensive understanding of the knowledge required to design optimal learning environments.

One example I have done recently was using Minecraft to design and build a research-based HBC fur trading fort that we went on a field trip to. They designed the landscape to resemble land around the Hudson Bay and studied the habitats of beavers. We then designed a game to play inside the Minecraft world that was representative of how the Canadian fur trade functioned.  Math was integrated throughout due to the fort construction and trading. We used the actual ratios for trade that the HBC used. Throughout the game-play kids had to convert different types and amounts of pelts into various quantities of trade goods represented in the game.

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.

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