Final entry – Analysis
At the beginning of the course, a lot of my attention was on more general educational challenges. Many of the themes that I picked out in the first few lessons were less about the math and science classroom and more about the kinds of issues educators were facing in their overall teaching practice. Ideas like needing more time, needing more professional development, how we build critical thinking skills in students and so on. Most of the courses I have taken in the MET program have had a more general approach and have not been subject specific. When I go back to the beginning of my e-folio, I notice that this mindset came into this course with me and took me a while to wash off.
As we continued into Module B, things started to shift. Learning about the different approaches to teaching in the math and science classroom specifically forced me into reflecting on my own practice in these subjects. Though I still was relying more heavily on my previous experience, my mindset definitely shifted. The Jasper Series and anchored instruction techniques really grabbed my attention because it was similar to the approach I use in my own practice. I gravitated to the GEM framework as I really liked the cyclical nature and this was where I started to explore what my classroom could look like if I opened up to take more risks and try out new approaches.
The last Module of this course really prompted me to explore platforms and tools that I had not yet before. As a teacher, sometimes being back in the learner’s seat is intimidating. Some of the platforms I found difficult to navigate and learn from, but this reminded me what it’s like to be a learner again. The final entries of my e-folio become a little bit more inquisitive. I noted that this was where I allowed myself to feel like a beginner again and to understand that it’s alright not to have all the answers. Moving forward, I will most definitely be incorporating more visualization platforms into my math classroom. Though in the past I have felt really confident with how I’ve taught math, I think that these platforms specifically could really benefit my students.
In trying to come up with a metaphor, I asked OpenAI (2025) to help me. The one that resonated with me the most was that for me, this learning experience has been like turning on the light in a room that you normally walk through in the dark. When this happens, you usually don’t turn on the light because you are so confident that you already know the way through the room. You’re not worried about tripping over something or missing a step because it’s a comfortable room for you. This is how my pedagogical approach to teaching math and science was at the beginning of the course. Turning on the light shows you how much more is in the room and how much has changed since the last time you turned on the light. I’ve gotten to experience so many new platforms and learn from so many of my peers that I can now see how much more I can do to expand my practice and benefit my students.
Reference:
OpenAI. (2025). ChatGPT response to a prompt about metaphors for becoming more open-minded [Large language model]. ChatGPT. https://chat.openai.com/
Week 13 – Info-Vis for STEM
One of the biggest questions that comes to mind when I think about the tools and resources for information visualization that are used in the math and science classroom, is how do we (as science and math educators) know which tool is the right choice for our context? For this topic, I chose to explore both NetLogo and Scratch. Though I found Scratch easier to wrap my head around, I think there are contexts where NetLogo could be extremely useful for students.
The first reading I did on this topic came from Finkelstein et al. (2005). Throughout their study of comparing computer simulations and in-person labs, they found that “students using the simulations learned more content than did students using real equipment” (Finkelstein et al., 2005, p. 6). Though evidently this isn’t always the case, this study showed that the possibility is there and that these “computer simulations can be as productive a learning tool as hands-on equipment” (Finkelstein et al., 2005, p. 1). There are many laboratory simulations available online, and one of these is PhET simulations from the University of Colorado Boulder. Gizmos and Labsters are also simulators that have been popular with educators. So again, the question arises, how do we pick?
The second reading I chose was from Amador & Soule (2015) and looked at how girls can build their excitement and motivation for mathematics using Scratch. Scratch comes from MIT and is a programming platform designed for beginners. This particular study found that “girls who took part in the computer-coding unit were excited about learning to code and using mathematics to accomplish their personal coding goals” (Amador & Soule, 2015, p. 414). What was also a win was the sense of ownership that Scratch allowed these students to feel (Amador & Soule, 2015). Programming is becoming part of all mathematics curriculum here in Alberta and there are many math educators who are not necessarily equipped to teach these skills. Utilizing an online platform like Scratch can help. Other examples of this type of software include Blockly and MakeCode, among others. Which one is best for middle schoolers? High school? What about students with differing learning abilities?
There are a plethora of platforms that can help educators provide meaningful learning opportunities for their students. Though it can be hard to decipher which of these platforms will suit the needs of our students best, by far the best place to start is simply by jumping in. Utilizing the experience of colleagues can be helpful and utilizing the expertise of students is also wise. We need not be extremely experienced with every platform that we share with our students but we do need to make the effort to try some out. So, as I grapple with the above question of which platform is going to be the right one, maybe the answer is in fact that they all are. So long as we work alongside our students with open minds, there are likely a number of platforms that can assist us in the visualization of material for our students.
References:
Amador, J. M., & Soule, T. (2015). Girls build excitement for math from Scratch. Mathematics Teaching in the Middle School, 20(7), 408-415
Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., & Podolefsky, N. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physics Education Research,1(1), 1-8.
Week 12 – Knowledge mobilization
Speculate on why role playing activities may not be promoted in math and science and elaborate on your opinion on whether activities such as role playing should be promoted.
Sadly, when we consider the stereo-types that go with the subjects of math and science, we think of rigor, and facts, and memorization, and often less creativity. Though those of us educators confident with these subjects know this not to be true necessarily, often individuals thrown into teaching them don’t think of utilizing some of the strategies often employed by the arts. One such strategy is role playing. Craciun (2010) describes role playing as something that can “help students to understand things from the perspective of another person,” (p. 175.) Utilizing such a strategy in the math and science classroom is not employed as frequently with older students as it is with younger ones. Though it can provide opportunities for students to “become more interested and involved, not only learning about the material, but learning also to integrate the knowledge in action,” role-playing is often thought of as a less “serious” way of learning in the math and science classroom. (Craciun, 2010, p. 175).
Using role playing in the science classroom seems to be a little bit more common amongst educators than the math classroom. Because of this, I attempted to find some examples of utilizing role playing for learning math. One that came up was the use of role playing in online math games from Ramadan & Setyaningrum (2022). They found that utilizing role playing in the context of these online games helped with both student motivation as well as the learning of mathematical concepts. Oldridge (2019) discusses the benefits of a “playful approach to math<’ by sharing that “playing and thinking are not at odds with each other.” Allowing students, especially in the older grades to experience play in the math classroom can benefit their thinking processes and can allow teachers to “guide students to engage with big and interesting ideas of mathematics,” (Oldridge, 2019).
In many ways, utilizing more arts-based pedagogical approaches in the math and science classroom invites in more knowledge mobilization. The learning becomes more social and in turn, more collaborative. Something powerful occurs when students are given permission to let down their guard and learn without the typical math and science stereotypes.
References:
Craciun, D. (2010). Role-playing as a creative method in science education. Journal of science and art, 1(12). 175-182.
Oldridge, M. (2019, July 24) The playful approach to math. Edutopia. https://www.edutopia.org/article/playful-approach-math/
Ramadan, S., Setyaningrum, W. (2022). Attractive ways to teach and learn mathematics using role-playing games: A literature review. AIP Publishing. https://doi.org/10.1063/5.0111155
Week 11 – Embodied learning
One of the most powerful takeaways from researching and reading about embodied learning has been from Winn (2003), in sharing that “our physical behavior often externalizes our thinking and extends cognition beyond our brain,” (p. 11). Human beings are not mind readers and thus the nature of embodied learning encompasses the physical aspect of learning as well as the visual aspect of learning. As an educator, when I see students at their desk, reading through a worksheet or textbook, I can only hope that they are understanding and learning the information in front of them. Embodied learning activities allow us, as educators, to visually see the ways in which our students are thinking. It is a method of thinking out loud without needing words. Winn (2003) goes on to discuss many examples of activities that utilize embodied learning, of which he discusses the idea of presence. This is “the belief that you are “in” the artificial environment, not in the laboratory or classroom,” (p. 14). This idea of presence is something that I think is required to get all the benefits available from embodied learning. Students need to buy-in and the nature of the activities needs to allow for this buy-in to occur.
One of the ways to create this buy-in can be to immerse students in the environment. Kamarainen et al. (2013) utilized embodied learning through environmental education field trips. Students were given the opportunity to experience augmented reality and utilize probeware to study different aspects of water. Though the water from the pond they studied could have been brought to them into their classroom, the augmented reality experience would not have been the same and thus immersing students in this kind of learning environment brought forward results of “a positive shift in their attitudes about their ability to understand focal topics and do science related skills,” (Kamarainen et al., 2013, p. 549). The nature of this learning experience required students to be physically involved with their learning experience.
There were many other examples of embodied learning experiences brought forward by Stevens (2012). For example, a complex plane is made life size so that students are able to physically navigate their own bodies through addition and multiplication problems (Stevens, 2012). Often when students come into a math classroom, they expect to be sitting at their desks working through problems either alone or maybe in a small group. An embodied learning activity is going to challenge these norms and allow students to utilize their physical bodies and the physical space of the classroom. The nature of this activity with the complex plane requires buy-in from students and that starts with the excitement and buy-in from their teacher. Embodied learning can be really powerful and even outside the box. It requires however, that students let go of their expectations and maybe even their previous understanding of how they learn in the math and science classroom.
References:
Kamarainen, A. M., Metcalf, S., Grotzer, T., Browne, A., Mazzuca, D., Tutwiler, M. S., & Dede, C. (2013). EcoMOBILE: Integrating augmented reality and probeware with environmental education field trips. Computers & Education, 68, 545-556.
Stevens, R. (2012). The missing bodies of mathematical thinking and learning have been found. Journal of the Learning Sciences, 21(2), 337-346.
Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114.
Week 9 – GEM pedagogy and T-GEM
Topic: Heat and energy transfer: tackling misconceptions about “cold” being transferred. Students have a hard time deciphering the fact that cold cannot transfer in the same way that heat can. Heat is a form of energy while “cold” is not. Students struggle to grasp that instead, “cold” is just the absence of heat. For some it occurs because this can be a challenging concept to “see,” and though videos can explain the movement of particles, some students need the hands-on experience to really understand a concept like this. I’ve found that providing opportunities for students to experiment has been a beneficial way for them to explore their misconceptions.
STEP 1: GENERATE
For this step, each student will get an ice cube. They will place the ice cube in their hand and watch it melt. I will then prompt them with the following questions:
- “What’s happening to the ice cube?”
- “What is happening with the heat of your hand and the “cold” of the ice cube?”
From there, students will write down a hypothesis with their ideas. They will then be placed into random groups of three and given a whiteboard to brainstorm with (Thinking Classrooms-style). They will share their hypotheses with one another and then collectively come up with a “rule” for how temperature changes when a warm and a cold object touch. As students are working together, I will circulate around the room, continuing to challenge their thinking and guide them if necessary.
STEP 2: EVALUATE
Kahn (2010) shares, “Some computer simulations are particularly valuable for science teachers because they help students’ visualize aspects of science that are either too large or too small for to view, afford rapid testing of ideas, reveal trends via graphs or other representations, and provide extreme situations to support thought experiments and what if scenarios” (p. 216). With this in mind, in their groups, students will be given a computer to bring up the PhET website, specifically the Energy Forms and Changes topic. This simulation allows them to view how when the individual is biking, the temperature of the water increases, and when the individual stops biking, the temperature of the water falls.
While they are observing this, I would ask them the following questions:
- “Where is the energy coming from?”
- “In which direction is the energy moving?”
- “Where does the energy go?”
Khan (2010, p. 223) discusses the importance of “encouraging students to make comparisons,” as well as sharing that “students were also asked to make comparisons,” (2007, p. 889). So, after experiencing and playing around with the simulation further, I will also add the questions:
- “How does this simulation compare to the experience of ice melting in your hand?”
- “In the simulation, which object is your hand? Which object is the ice?”
Students will be given time to explore the different types of energy input that the simulation allows for and discuss their reasoning for changes that occur.
STEP 3: MODIFY
From here, students will head back to their whiteboards to look at the initial “rule” they came up with. They will be asked to make any changes they think are necessary to their rule now having the experience of viewing the simulation and comparing it to the ice melting activity.
This cycle could continue with different experiments that would help foster additional reflection, conversation and inquiry.
Here is the diagram I created for this cycle. I chose to have building inquiry skills in the centre as this is the heart of the T-GEM approach. I also chose to use the language of “thinking” within each step of the diagram because this is always at the centre of my classrooms. Students know that when they step into my room, they are going to have to use their brains. Lastly, I chose to have technology all around the GEM cycle because the T in T-GEM can truly occur at any stage.
Week 8 – The Learning for Use (LfU) framework
Tackling Earth Science misconceptions: Why the Learning for Use framework can provide support
A number of conceptual challenges exist amongst students in the field of science education today. Among them and frequently, the study of Geology and Earth Science. There are particular skills that go along with these types of studies such as geospatial reasoning and awareness. Perkins et al. (2010) discuss how “there is a growing consensus that spatial literacy plays an integral role in our ability to process information and provides a framework for understanding that crosses disciplines and contexts” (p. 213). Perhaps more of this type of study could support the decrease of misconceptions in the fields of Geology and Earth Science. A powerful way to also contribute to this decrease is applying the Learning for Use (LfU) framework as discussed by Edelson (2001).
Students don’t know what they don’t know and the LfU framework can play a vital role in helping students in identifying these areas. Many scholars have written about the challenges in teaching Earth Science. For example, Hannula (2023) discusses how there are a number of Earth Science concepts that are often left out of curriculums. King (2010) discusses the high level of error and misconceptions that exist in science textbooks in England and Wales, particularly when covering topics in Earth Science. Pyle et al. (2017) discuss the misconceptions that creep up when teaching the Solid Earth curriculum. The three steps identified by Edelson (2001) for implementing the LfU framework include: “motivation,” “knowledge construction,” and “knowledge refinement” (p. 358). Each of these steps can support students in better understanding Earth Science.
Motivation
Edelson (2001) discusses how the kind of motivation needed in the LfU approach is not the kind that is often referred to in more general education terms. This type of motivation “occurs when one comes up against a limitation or a gap in one’s knowledge” (Schank, 1982, Berlyne, 1966, as cited by Edelson, 2001, p. 358). When students have misconceptions about Earth Science topics, having these misconceptions identified and then presented with a challenge on figuring out the truth can create “a content in memory for integrating new knowledge” (p. 358). This is a circumstance presented to students, within the LfU approach where they can be motivated to tackle their own misconceptions.
Knowledge construction
Now not all of what students know about Earth Science is misconceptions. There does exist prior knowledge that can be built upon and strengthened when using the LfU approach for knowledge construction. In fact, that existing knowledge must be linked to the new knowledge structures that are being taught in order for them to take up memory space (Edelson, 2001). Edelson shares that “this step in the LfU model recognizes incremental knowledge construction as the fundamental process of learning” (p. 358). Incremental being the key word here… Using the LfU framework means meeting students where they are at and slowly but surely building them up.
Knowledge refinement
Though all steps are important, when combating misconceptions, this step may take the cake. Here Edelson (2001) shares that “knowledge is reorganized, connected to other knowledge, and reinforced to support its future retrieval and use” (p. 359). When we discuss why students have misconceptions in science, it can at times be because they don’t remember exactly how something was taught to them. Being able to successfully and accurately retrieve prior knowledge will very much benefit them. This final step in the LfU framework actively works to tackle misconceptions.
References:
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.
Hannula, K. (2023) Challenges and opportunities for K-12 earth science education. Journal of Geoscience Education, 71(2), 127-128.
King, C. J. H. (2010). An analysis of misconceptions in science textbooks: Earth science in England and Wales. International Journal of Science Education, 32(5), 565-601.
Perkins, N., Hazelton, E., Erickson, J., & Allan, W. (2010). Place-based education and geographic information systems: Enhancing the spatial awareness of middle school students in Maine. Journal of Geography, 109(5), 213-218.
Pyle, E., Darling, A., Kreager, Z., & Howes, S. (2017, December 8). Research on students’ conceptual understanding of Geology/Solid Earth science content. The National Association of Geoscience Teachers. https://nagt.org/nagt/geoedresearch/grand_challenges/wg1.htmlLinks to an external site.
Week 7 – SKI and WISE reflection
The motivation for WISE largely came from the need to incorporate inquiry practices into the science classroom. As Linn et al. (2003) discuss from Becker (1999) and Horizon (2001) “most states and national standards call for inquiry instruction, few science classes include inquiry practices.” Because of this need inside classrooms and for teachers, the Web-based Inquiry Science Environment (WISE) was created. When the word inquiry is used throughout the WISE projects, this relates to the type of pedagogy “where students design solutions to problems, generate predictions before conducting experiments, use scientific evidence to support theories or conclusions, debate contemporary science issues, and reconcile differences between new and prior scientific ideas” (Williams et al., 2004).
The Scaffolded Knowledge Integration (SKI) framework is utilized throughout WISE projects because of its ability to help promote lifelong learning of scientific concepts (Linn et al., 2003). The SKI framework is structured on four main points: “(1) making thinking visible, (2) making science accessible, (3) helping students learn from each other, and (4) promoting lifelong learning” (p. 524). The beauty of teaching alongside a WISE project is its ability to be tailored to each individual classroom’s needs. WISE utilizes “flexibly adaptive materials” and enables “local adaptations” in order for it to meet the needs of diverse learners and teachers (Linn et al., 2003, p. 518). The development of the WISE projects involves heavy emphasis on the idea of scaffolding in order to support students with steps that are neither too broad, nor too specific (Linn et al., 2003).
There are a number of similarities between the WISE projects and the Jasper series that we discussed in prior weeks. For one, the idea of creating life-long scientific learners is at the core of them. Though they both take on different styles of pedagogy and center on different frameworks, at the heart of these two programs is the desire to keep students interested and engaged in their science classrooms. Multiple approaches are used when implementing the Jasper series, of them, in my opinion, the most similar to the WISE projects would be “structured problem solving” (Cognition and Technology Group at Vanderbilt, 1992). Providing students with basic facts alongside their exploration of the tasks given resembles the level of scaffolding designed into the WISE projects.
There are many WISE projects that would work alongside the curriculums I teach at the middle school level. To begin, I think I would choose to use a WISE project for early finishers. These students are typically really interested in the topics being discussed as so would likely be keen to engage and research further. This would also provide me with feedback on the projects as I would be able to engage with students as they work their way through the sections. In the future, I would love to integrate a WISE project into my teaching with a full classroom of students. I would choose to localize the content through the editing features on the WISE platform, making the content more relevant to the area in which I teach and the cultures of students in the classroom. I would also ensure the use of a feature like Google Read&Write was accessible on all devices for all students. The WISE projects provide a great opportunity for students to practice their inquiry skills while also engaging with technology in a motivating and compelling way.
References:
Linn, M., Clark, D., & Slotta, J. (2003). Wise design for knowledge integration. Science Education, 87(4), 517-538.
Williams, M. Linn, M.C. Ammon, P. & Gearhart, M. (2004). Learning to teach inquiry science in a technology-based environment: A case study. Journal of Science Education and
Week 6 – Reflection on the anchored instruction symposium
After reading through the multiple perspectives of my classmates in the anchored instruction symposium, it is clear to me that the kids are in fact alright. What I mean to say is that, the interest and level of eagerness to adapt to the needs of our students is very much present. There were a few themes I noticed within the contributions from my classmates:
- Time. Many of the postings shared just how fascinating they found the Jasper series to be and how if they had more time, they would create videos relevant to their own subjects and grades that could be implemented. Many classmates even shared their wicked ideas about what kinds of problems they would assign their students. If this approach of anchored instruction is so effective, perhaps school boards will consider providing opportunities for teachers to explore the approach more and give them time to create some of their own problem-rich resources.
- Real-world context. Many of my classmates agreed that the need for real-world context, especially in the math classroom, is critical. Because math can be such an intangible subject, situating and contextualizing the learning for students is of utmost importance. Vye et al. (1997) found that having strong contexts for students to learn from supported more transfer than more traditional styles of learning.
- Collaboration. Gone are the days of struggling through math problems alone. The idea of working in groups was brought up in multiple postings by my classmates. And if one works in a classroom with students, it’s easy to see why. When the right learning environment is created, students are able to collaborate and problem-solve as a team. They build more than just the math skills, they build the skills of considering others perspectives, of defending their ideas, of actively listening to other positions and vantage points, among so many others.
Overall, the Jasper series and the approach of anchored instruction showed us how interesting and engaging the math classroom can really be. It seems as though my classmates and I are ready to elevate our practices by bringing some of these ideas to life in our own contexts and classrooms.
Reference:
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.
Week 6 – Anchored instruction symposium
What evidence exists regarding anchored instruction and its effectiveness as a pedagogical design?
In her 2021 article, Anchored Instruction, Kathryn Cook discusses the research conducted on the topic and provides evidence of its effectiveness. Bottge et al. (2004) as cited by Cook (2021) shared that “students were better able to maintain and transfer what they learned several weeks later when compared with students taught with traditional word problems.” Cook (2021) also shared from Glaser et al. (1999) that students were more engaged with the learning process when taught using anchored instruction as student-teacher interactions more than doubled. Anchored instruction allows space for collaboration and cooperation. The Cognition and Technology Group at Vanderbilt (1992) shared that “cooperative learning and cooperative problem-solving groups enhance opportunities for generative learning” (p 68). This kind of learning requires difficult problems, and when a group member “can provide meaningful explanations to their partners, problem-solving improves over individual performance” (Webb, 1989,1991 as cited by Vye et al., 1997, p. 439).
What are some important nuances of the research that are pertinent to your practice?
The most pertinent takeaway of the readings on the Jasper series, for me, was that it really requires pedagogical practice. As Vye et al. (1997) discuss, for anchored instruction to be successful in the classroom, the teacher needs to facilitate the environment that supports it. Sharing ideas, being open to trying new things, and feeling confident explaining yourself are just some of the norms that need to be present in order for a pedagogical technique like anchored instruction to function at its best and most effective. As much as we can hope our students are going to take on challenges like this with an open mind, the reality is this is not the environment they are used to in the math classroom specifically. As such, it is going to take practice as both the teacher and the student in creating a classroom culture that will encourage anchored instruction.
What further inquiries or questions does the research reported in the articles raise for you (e.g. regarding evaluation, professional development, disabilities and/or the content area you teach or would like to promote etc)?
The most significant question that this research has raised for me, is how we, as educators, can become skilled enough to implement anchored instruction to be at its most impactful. Evidently, there is a need for professional development in this area. Vye et al. (1997) share from Ball & Rundquist (1993) and Heaton & Lampert (1993) how educators often don’t actually have enough mathematical and pedagogical knowledge to successfully implement this type of learning. As transformative as anchored instruction may be, teachers need to feel confident with the approach and capable of facilitating learning in an inquiry-based and contextual environment. Could mentorship be something useful to help teachers newer to this approach? We cannot become experts overnight, so there is a need for supporting teachers to master this method.
Finally, in what ways might a current technology for math (Eg. IXL Math, Dragonbox, Math Genius or others) relate to this question?
After looking for a few different technologies, I came across MathVC. It is an LLM-powered virtual classroom that can help real-life students work on strengthening their mathematical modelling (MM) skills. MathVC provides the opportunity to collaborate and effectively discuss math modelling when in-person, classroom opportunities are not possible. Similar to the anchored instruction technique, working in groups is prioritized and foundational to MathVC. The argument made from the creators of MathVC is that “practicing the MM skill is often the most effective when students can engage in group discussion and collaborative problem-solving” (Yue et al., 2025). The Jasper series takes on a similar challenge in having students work in groups to come up with solutions. The reality is, in order to prepare our students to enter the workforce, they need to be able to successfully collaborate. Allowing opportunities for these skills to be practiced alongside curricular topics is a powerful way to implement anchored instruction.
References:
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.
Cook, K. (2021). Anchored instruction. EBSCO. https://www.ebsco.com/research-starters/social-sciences-and-humanities/anchored-instruction
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.
Yue, M., Whenham, L., Suh, J., Zhang, Y., & Yao, Z. (2025) Math VC: An LLM-simulated multi-persona virtual classroom for collaborative mathematical problem solving. https://arxiv.org/pdf/2404.06711
Week 6 – The Jasper series
The Jasper series is a pedagogical method designed to get students thinking, problem-solving and collaborating. It is rooted in anchored instruction, a technique described by the Cognition and Technology Group at Vanderbilt (1992) as being “situated in engaging, problem-rich environments that allow sustained exploration by students and teachers” (p. 65). After watching a series of videos, students are tasked with solving a problem in a realistic context. Working alongside their classmates and teacher, they come up with solutions that might work for the problem they were given. There are three models for teaching the Jasper series in the classroom setting outlined by the Cognition and Technology Group at Vanderbilt (1992):
- The basics first approach. This model requires students to refine their basic skills in the areas that they will need to solve the problems they will encounter within the series. This method, to me, seems the least engaging for students, but the most comfortable for educators. This means students will all approach the problem in a similar way because they will have been taught the basics in a similar way. There will be less opportunity for creativity. That said, students will likely have more confidence in their approach, meaning they might require less teacher guidance.
- The structured problem solving approach. This model teaches the basics alongside the series. The reasoning behind this is to motivate students to learn the basics so that they may solve the problems they are given by the series. In my opinion, this method opens the door for more creative and collaborative problem-solving as there is opportunity to try things out before being told by the teacher what to do. Having the skills taught simultaneously will still maintain a level of confidence for students and provide them with a safety net when they aren’t sure what to do next.
- The guided generation approach. This model really allows students to explore their own problem-solving as teachers very much take a backseat. There are very few restrictions to this approach and “the ultimate goal is to remove as many scaffolds as possible” (Cognition and Technology Group at Vanderbilt, 1992, p. 77). As someone who has tried out a similar approach in the classroom, this kind of teaching usually leaves students feeling uncomfortable because it is not what they are used to. That said, with an open mind, students are often able to be the most collaborative and creative through this kind of model.
Overall, this series reminds me a lot of the Building Thinking Classrooms methodology from Peter Liljedahl, a method I use in my math classroom all the time. As an educator, I appreciate the resilience building that these types of pedagogical approaches allow for. Allow space for my students to be comfortable to struggle and problem-solve are key in their development as critical thinkers.
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.
Week 5 – Design of technology-enhanced learning environments (TELE)
The definitions that appeal the most to me are the ones from Roblyer (2012) and from the Association for Education Communications and Technology (AECT). When I think of education technology, I think of the two applications that are described by AECT and mentioned also by Roblyer (2012). Firstly, the methods we use technology for, what actions we take with them, and how they aid in the processes of solving problems. And secondly, the actual tools or resources that are used for these methods and applications. At the core of my own definition of educational technology is how and what we use to help students build the skills necessary to think critically and solve problems. The part of Roblyer’s (2012) definition that says “technology is us” is also quite powerful. In the year 2025, rarely are we doing anything without the use of modern day tech. We live our everyday lives in technology-enhanced learning environments (TELE). This is true in the classroom as well. Tech is constantly being applied to pedagogical choices to find more diverse learning solutions. In the math and science classroom more specifically, educators employ technology to make learning experiences more authentic. TELEs allow for students to apply their learning into more real world experiences. For example, utilizing Google Earth to learn about climate change, or using a Google Sheet to learn about compound interest with the latest bank rates. Students respond well to TELEs because of how integrated technology is into every other aspect of their lives.
Reference:
Roblyer, M.D. & Doering, A. (2012). Integrating educational technology into teaching, (5th Ed.). Upper Saddle River, New Jersey: Prentice Hall.
Week 3/4 – Interview analysis
Mrs. A is in her 21st year of teaching. She has spent all of her career at the middle school level in both the French Immersion and English side of schools. Mrs. A noted how she likes to switch things up frequently and so, has taught many different subjects. She is currently in a learning support role, teaching specifically literacy and numeracy skills.
As I continue to look deeper into these questions and read more of my peers findings, I have noticed a couple of trends coming up.
Firstly, teachers are concerned about access. Not all schools are equipped to facilitate one to one technology for each student. Schools encourage students to bring their own device, however this brings up a whole other level of access. Not all families can afford for their children to have their own device. This means some students come to school with a device and some do not. Though this reduces the amount of students who need to borrow a device from the school, it means that these same students don’t have access to a device at home. A number of teachers shared that they really noticed a discrepancy in access to technology during Covid, and these discrepancies continue to persist in today’s classroom.
Next was the idea of more professional development. Many interviewees, including the two that I spoke with, shared their interest in more professional development opportunities surrounding educational technology in the science and math classrooms. Though these opportunities exist, often they are not subject specific or they are opportunities where multiple different technology options are provided and teachers aren’t given the time to really explore and learn how to use them. From the interviewees perspectives, this can act as a barrier as to why technology doesn’t always get integrated in the classroom. So it seems that it isn’t that teachers don’t want to use new technology in their classrooms but they note that they need more support so they feel confident with it’s implementation.
As I continue to learn more about technology in the math and science classroom, it appears that there is a high level of interest in it, though I’m learning that there exist a number of barriers to its successful adoption. Moving forward, I would like to learn how I can be both an advocate and an ally in removing some of these barriers for my colleagues. Given my experience and education with technology, I’d like to know how I can support the professional growth of the teachers in my own building. This would mean really understanding the needs and levels of the teachers in my building and facilitating opportunities for mentorship. I would be able to help reduce the barriers they feel towards implementation and support them in feeling confident to use more technology in their pedagogical practice.
Week 2 – Unpacking assumptions
What “counts” as good use of technology in math and science learning environments?
- Allows students to imagine their learning outside of the classroom walls
- Gives students a more equitable learning experience
- Provides opportunities for learning that might not have been possible without tech
- Empowers students to try new things
- Empowers students to feel confident in what they know
Good use of technology in the math and science classroom looks like excitement. It sounds loud with conversation about things that students are discovering using technology, things that can’t be learnt through textbooks or teachers. Good use of technology feels like students are confident and empowered to take chances, make mistakes, and discover what they don’t know. On a less abstract level, good use of technology is well thought out. It enhances the learning environment for students without becoming the center of the learning experience. So often, students can misuse technology or can find themselves more enamoured with the gamification aspect. Though these types of programs have a place in our math and science classrooms, good technology use is going to allow students to tap into those higher order skills.
Educators don’t have a lot of time on their hands, and these days, less and less. Good technology use is going to help educators understand their students’ needs better. Whether it’s a quick formative check-in, or a more in depth analyzation of conceptual challenges, good technology in the math and science classroom provides educators with support for their students’ academic growth. Technological needs are contextual. What might be a great use of technology one day, might not work the next. As much as it is on the teacher to incorporate technology into the classroom, the responsibility of good technology use also lies with the students. So though I haven’t given a concrete example of good technology use in the math and science classroom, I think the important thing to remember is that it needs to be dynamic and intentional.
Week 1/2 – Conceptual challenges
Conceptual challenges in the science and math classroom are often plenty. Student’s come to us with their preconceived ideas and though often, there are parts of them that resemble the actual concept, they are laced with misunderstandings gained from personal experiences, previous education, or even ideas from their imagination. Though we weren’t explicitly told where Heather’s misunderstandings came from, it is evident that she was very firm in her beliefs of bouncing light and initially, her belief of how earth orbited the sun. What registered most with me from A Private Universe was when Heather’s teacher, Marlene, discussed how as educators, we aren’t always privy to the things our students are grasping or thinking. This can make it challenging to address misconceptions.
Fosnot (2005) explores how these “contradictions” in what students think they know versus what the actual concept is, “need to be illuminated, explored, and discussed” (p. 25). The challenge here is being able to identify students’ contradictions and misconceptions before they are too self-conscious to admit them and before they become too ingrained in their cognitive understanding. As an area of further research, I wanted to see ways in which these misconceptions can be identified. Soeharto et al. (2019) shares from Gurel et al. (2015) how “a combination is better than a single method” when looking to identify common misconceptions in science (p. 259). These methods can include interviews, multiple tier tests and multiple choice questions (Soeharto, 2019). So, with this in mind, would it be possible to attempt to identify the common contradictions in a science class at the beginning of a term, and then purposefully address them throughout the course? This is where technology could come into play with the ability to analyze the results and identify the contradictions that would align most closely with the course content.
Having a deeper understanding of what knowledge our learners are bringing into our classrooms could have a great impact on our ability to ensure they move forward with legitimate information and learning. Erickon (1979) shares that “the most important single factor influencing learning is what the learner already knows” (p. 221). If this is the case, why are we not spending more time identifying this when we first meet our students? Though we can assume a new sixth grader is coming into our classroom knowing the concepts of the fifth grade curriculum, it seems it would be a disservice not to try and pinpoint more accurately what misconceptions exist so they can be better addressed and opportunities can be provided for them to be challenged.
References:
Erickson, G. L. (1979). Children’s conceptions of heat and temperature. Science Education 63 (2), 221-230.
Fosnot, C. (2005). Constructivism: Theory, perspectives, and practice. Teachers College Press. https://go.exlibris.link/QnnMtSbC
Harvard-Smithsonian Center for Astrophysics. (1987). A Private Universe [Video]. Annenberg Learner. https://www.learner.org/series/a-private-universe/1-a-private-universe
Soeharto, S., Csapó, B., Sarimanah, E., Dewi, F. I., & Sabri, T. (2019). A review of students’ common misconceptions in science and their diagnostic assessment tools. Jurnal Pendidikan IPA Indonesia, 8(2), 247-266.
Week 1 – Auto e-ography
You can find my auto e-ography here. And, for those curious about these infamous Plickers cards, you can see what they’re all about here.