Author Archives: shayla mangat

Primary Geometry Lesson

Srinivasan, et al. (2006) describe the learning process as described by the learner’s prior knowledge, ability and motivation. The amount of load placed upon the students working memory by a learning task, “cognitive load”, enhances or diminishes their individual learning experience. Not only do educators need to account for this appropriate cognitive load, they are also searching for effective tools to motivate students. Some of the factors influencing student motivation include: challenge, fantasy, curiosity, novelty, interest, and importance/value. Additionally, educators search and explore digital technologies and/or virtual simulation to further enhance the learning experience. As described by Finkelstein, et al. (2005), these digital tools provide visual representations of hidden concepts. Effective digital tools/simulations are designed to be highly interaction, engaging, highly visual, build explicit bridges between students’ everyday understand of the world and its underlying physical principles, and make physical models visible.

The below unit plan takes Sinclair and Bruce’s (2015) findings that “students perform quite poorly on a wide range of geometry tasks” (p. 319). They found that almost every country based their primary school geometry curriculum on the study of two-dimensional shapes. They reason that educators fail to see that geometry provides the basic meanings of mathematics: representations, models, visualizations, analogies and physical materials). Incorporating the digital, social, inquiry and visual nature of each of the instructional frameworks from Module B, my goal is to create a unit that is engaging and motivates my students with playful tasks and exploratory lessons.

Topic: 3-D Geometric Shapes

Grade: 2

Motivation/Hook: Accessing previous knowledge

While holding up models of a 3-D shape:
- What does this shape remind you of?
- What shapes do you see?
- How are they connected?
Scavenger hunt: Can each table group please find me two items in the classroom that has this shape? How did you know these were the same?

Familiarity:

In pairs ask students to group the shapes without providing any criteria for alike shapes.
- Why did you choose these groups?
- How are these similar or different?

Teacher Guidance:

Introduction of edges, faces and vertices (shape attributes)
During group discussion, provide each student with the shape for students to twist and manipulate (visual and kinetic interaction)

Technology Integration: Virtual Manipulation

Example tools provided by Sinclair & Bruce (2015)
- Kidpix, Piece Puzzler, Geometer’s Sketchpad, Cabri-geometre
Shape manipulation through tough screen and dragging
- Is it the same shape if a stretch it? What if I rotate it?

Research has indicated that young students are more creative and create more complex and prolific patterns when using virtual manipulation than when using concrete materials. This may be because the shapes can be snapped into position and stay fixed (you can stack to spheres on top of each other without them falling over) (Sinclair & Bruce (2015).

Applying Understanding

Students use the above tools to design and create a 3-D character or object
- Why did you choose these shapes? How would these shapes stay together? What different sizes did you choose?
3-D printer to bring their vision to life (aided by an older buddy class).

Finkelstein, N. D., Adams, W. K., Keller, C.J., Kohl, P.B., Perkins, K. K., Podolefsky, N. S. & Reid, S. (2005). When learning about the real world is better done virtually: a study of substituting computer simulations for laboratory equipment. Physical Education Research. 1(1), 1-7.

Sinclair, N. & Bruce, C. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education. 47(1), 319-329.

Srinivasan, S., Perez, L., Palmer, R., Brooks, D., Wilson, K. & Fowler, D. (2006). Reality versus Simulation. Journal of Science Education and Technology. 15(2), 137-140.

Constructing Knowledge & VFT

How is knowledge relevant to math or science constructed? How is it possibly generated in these networked communities? Provide examples to illustrate your points.

Learning science involves young people entering into a different way of thinking about and explaining the natural world; becoming socialized to a greater or lesser extent into a practice of the scientific community with its particular purposes, ways of seeing, and ways of supporting its knowledge claims (Driver, et al, 1994, p. 8)

Throughout our readings this term, we have been exposed to the constructivist position of knowledge acquisition. Driver, et al. (1994) once again explain that “the core commitment of a constructivist position [is] that knowledge is not transmitted directly from one knower to another, but is actively build up by the learner” (p. 5). They argue that there are three essential factors of this approach in learning science in the classroom: personal experiences, language/symbolism, and socialization.

Referencing both Vygotsky and Piaget, there is an emphasis on the social nature of learning in the classroom. Students require the conversations with peers and adults as they develop a common language to represent scientific symbols, and common sense knowledge. As students participate in active, physical experiences, and are exposed to everyday language and are able to evolve their understanding to make sense of the natural world. For example, students have a commonly help conception that a constant force is necessary to maintain an object in constant motion. Experiences such as pushing a heavy object or pedaling a bicycle allow students to develop these informal, common sense ideas.

Following the ideas of the Jasper project, LfU, T-GEM, science educators are seen as facilitators who make the cultural tools of science available to learners and supports their construction of ideas through discourse about shared physical events. As students work with hands-on experiments, educators pose questions, participate in shared discourse, introduce new ideas, and support and guide as the class participates in shared knowledge.

Another form of exposure to knowledge comes in the form of field trips. With the development of multimedia projects, researchers investigate the use of virtual field trips as a replacement for traditional field trips (Spicer & Stratford, 2001). Using a problem-based approach, researchers developed a hypermedia package, Tidepools’. In one sitting, students spend 2-3 hours individually exploring how animals might respond to low oxygen during low tide periods. When completed, students reported a positive reaction; stating that is was an enjoyable way to learn. They were however, unanimous in their view that it was not a substitute for a real field experience. They felt that it lacked the complexity of a real experience and the collaboration with peers.

Below are a few ways that VFT could be utilized in education:

Prepare for Geography field trips.
Complement and enhance a real field trips (enhance preparation and act as a revision tool after a field trip).
Explore familiar territory at their own pace.
Museums and other informal environments that are not local.
Allow for multi-visiting opportunities (Yoon, Elinich & Wang, 2012).

Are there other ways that we could use VFT to enhance student learning experiences?

Driver, R., Asoko, H., Leach, J., Mortimer, E. & Scott, P. (1994). Constructing scientific knowledge in the classroom. Educational Researcher, 23(7), 5-12.

Spicer, J. I. & Stratford, J. (2001). Student perceptions of virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17(1), 345-354.

Yoon, S., Elinich, K. & Wang, J. (2012). Using augmented reality and knowledge-building scaffolds to improve learning in a science museum. Computer-Supported Collaborative Learning, 7(1), 519-541.

Embodied Learning and Gesturing

When I search the term embodied learning on Google, it is defined as “Embodied learning is an educational method that has been around for a while in (primary) education. In this method, one does not only offer an intellectual way of teaching, but also involve the whole body. One can think of e.g. doing math while throwing small bags of sand to each other”. I am taking from this the importance of engaging the body as a whole.

Winn (2003) discusses the interaction between a person and their environment. It is specified that this interaction is not just the brain processing the environment; however, it is the entire body that uses the senses to interact with the surroundings. As Kim, Roth and Thom (2010) state “when asked to talk about knowledge, many individuals point to their heads as if to suggest that this is where knowledge resides” (p. 207). Their study found that children’s bodied constitute an integral part of knowing thinking, and learning. As well, they found that students engaged in co-gesturing which allowed for a collective understanding.

As I think of my students, I completely agree that their learning is enhanced through their physical movements. For example, we were completing a unit on 3-D geometric shapes. I recall holding up a triangular prims and asked students what 2-D shapes made up this 3-D shape (rectangles and triangles). I watched as some of my students began using their hands to create the shape before answering. The motion/gesture of creating the shape allowed them to recall from their memory the name. It would be my guess that their previous teachers had them creating the shapes with their hands or other objects while learning the shapes.

Referring back to the above definition, it refers to embodied learning as a form of hands-on learning primarily done in primary grades. Is embodied learning and hands-on-learning the same thing? Does the definition provided by google truly encompass all that is embodied learning? In your experience, where have you asked students or seen students use gestures as a way of expressing their knowledge? Did you present the gesture to the student as a way of processing information? Or did they create it themselves/collaboratively with others?

Shayla

Kim, M., Roth, W. M., & Thom, J. (2011) Children’s gestures and the embodied knowledge of geometry. International Journal of Science and Mathematics Education, 9(1), 207-238.

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

Module B Synthesis

Jasper Project	– Video-based tool. – Visual representation of information. – Embedded data design and immediate feedback. – Students work through identifying and creating goals and sub-goals to solve a presented problem (problem-based learning). – Cooperative learning experience in small groups. – Potential for teleconference assessments that rejects paper-to-pencil tests and explores students using descriptive, problem-solving skills to answer real-world questions.
*SKI & WISE*	– Online activities. – Inquiry based approach. – Students taking on roles of professionals. – Self-paced. – Students are able to choose topics that fit these interests and needs.
*LfU & My World*	– Inquiry based approach. – Four central principles: importance of construction and modification of knowledge structures, goal-directed, environmental/circumstances effects future retrieval, that support use before it can be applied. – Steps: motivation, knowledge construction and knowledge refinement. – Linking new knowledge to old knowledge.
*T-GEM & Chemland*	– Inquiry based approach. – Cyclical design. – Students work through creating hypotheses and engaging with material to modify their mental models. – Steps: generate, evaluate, modify
*Common Themes*	– Increased student motivation – Collaborative learning. – Learning experience enhanced through the use of technology. – Inquiry based approaches. – Visual representations of information. – Teachers promote deep and robust learning experiences.

As I reflect on the four technology-enhanced learning environments, I believe that each of these approaches would have a positive effect on my students. Each providing its unique approach to learning, yet each allow students to explore through questions and exploration of information. Research has indicated that these environments are effective for engaging students and allowing them to be active learners. They prepare students to become lifelong learners “by engaging them in carrying out complex projects and regularly critiquing, comparing, revising, rethinking, and reviewing their ideas” (Linn, Clark, Slotta, 2011, p. 532). They move science and math past textbooks and tests, and utilize technology to provide students with real-life scenarios. Additionally, each follows a view of constructivism and utilizes Vygotsky’s zones of proximal development by having students work in groups and learn from each other.

Although these environments seem to be set for higher grades, the common themes seem to follow those of any grade levels. I do believe that it would take time and trial-and-error to alter these to fit the needs and abilities of my students. Has anyone discovered any tools that may be similar to these that would work more closely with elementary students?

Shayla

T-GEM – Measurement Gr. 2

This lesson was creating using the T-GEM process for our measuring unit in grade two. To begin my lessons, I start by discussing non-standard units of measurement. This is where students get to explore using paper clips, cubes and other tools to measure different objects around the classroom, school. In my experience students become really excited to do this and it is a fantastic way to have students work in pairs or small groups towards a common goal. By the end of the non-standard unit, I need to ease my students into standard units of measurement and using a ruler. Each students already has a ruler in their desk but at the beginning of grade two it is usually used for drawing straight lines as students do not yet understand what the lines on the ruler represent. I believe that this is where the GEM process would repeat as we move from non-standard measurements of unit, to standard measurements (mm, cm, m).

I have to say that I enjoyed creating this lesson. It is simple, but an important topic for students to learn and be excited about as the units become bigger and conversation begins in older grades. What I appreciated most about the GEM process was the cyclical fashion that the information and inquiry is presented. As teachers probe with questions and what if statements, students are provided the opportunity to explore and engage with the material and modify their mental models as they progress (Khan, 2007). As well, technology can be used to expand students learning to answer extreme values, visualize the information, produce data quickly and generate graphical trends (Khan, 2011). I have set up this unit without digital technology; however, I think it would be a fantastic to add in distances (km) using maps and other tools when students begin to realize that cm will only get them so far.

I have uploaded my cycle onto google docs:

https://docs.google.com/document/d/1qOMT_oapac8IQynxZnW4-kmzC33Q48dEPkcD2x0YneM/edit?usp=sharing

Khan, S. (2007). Model-Based Inquiries in Chemistry. Department of Curriculum Studies, Faculty of Education, University of British Columbia. 91(6). 877 – 899. doi: 10.1002/sce.20226

Khan, S. (2011). New Pedagogies on Teaching Science with Computer Simulations. Journal of Science Education and Technology, 20(3), 215-232.

LfU and Math

In what ways would you teach an LfI-based activity to explore a concept in math or science? Draw on LfU and My World scholarship to support your pedagogical directions. Given its social and cognitive affordances, extend the discussion by describing how the activity and roles of the teacher and students are aligned with LfU principles.

I would like to start off by saying how much I enjoyed this week, especially the working with the article Learning-for-Use: a framework for the design of technology-supported inquiry activities written by Daniel Edelson (2001).

The LfU model provides students and educators with a framework with the aim of supporting deep and robust learning experiences. The framework follows four central principles: importance of construction and modification of knowledge structures, goal-directed knowledge construction, environmental/circumstances of knowledge construction effects future retrieval, and knowledge must be constructed in a form that supports use before it can be applied. To achieve these principles, the LfU outlines three fundamental steps toward knowledge application; motivation, knowledge construction and knowledge refinement.

As I read through the example provided by Eldelson, The Create-a-World Project, I started creating my own project along the margins of my paper. His paper focuses on the inquiry process in science classrooms but I wonder if I would be able to implement similar steps in math. I wanted to focus on math because I already feel that I have been successful in integrating inquiry into my science curriculum; however, I feel that I am still struggling to provide these deep learning experiences for my students in math. Reflecting on my own learning experiences in math, the content for this project would focus on probability in upper elementary grades.

To motivate my students and have them excited to learn about probability, I would like to begin with a card trick. One of those card tricks that have students scratching their head, questioning how it is possible but simple enough that students would be able to figure out how it was achieved. Without providing any answers, I would assign each students into a small group, provide each group with a deck of cards, and have them work together to recreate the trick. As students develop their communication skills and begin the inquiry process (questioning and exploring), I would observe and find the misconceptions that my students have. The second stage in the LfU model is knowledge construction and linking new knowledge to existing knowledge. During this phase I would introduce my students to important terms, address the misconceptions I had observed, and we would work through the steps of probability. Additionally, I would like to have students simultaneously adding to a thought blog as a way of incorporating technology to record students learning process. The final step is knowledge refinement and reflection. In this stage I would reintroduce students to the existing card trick (maybe a new one?) and have them apply the information they have learned to work through a new problem or create one of their own.

This is only the skeleton of a unit, but the readings this week are making me very excited to try it out. Any suggestions on how to add to these ideas? In what ways could I use more technology (or is it necessary)?

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

WISE about RIDES

Following the Jasper Project readings, I was excited to explore another platform to extend student learning. The Web-based Inquiry Science Environment (WISE) provides students with an individualized learning experience catered to themselves. Having tried out the program, I do believe that it has a lot of benefits, but like any resource it has some faults.

Linn, Clark and Slotta (2002) define this inquiry learning as “engaging students in the intentional process of diagnosing problems, critiquing experiments, distinguishing alternatives, planning investigations, revising views, researching conjectures, searching for information, constructing models, debating with peers, communicating to diverse audiences, and forming coherent arguments” (p. 518). Using a scaffolded approach, the program sets to make thinking visible, making the science accessible, helping students to learn from each other, and promote lifelong learning. They believe that the learning is accessible by providing information that is relevant to the students. The authors state that WISE invites students to report their ideas, teachers to provide feedback, and the creation of models, simulations, and other representatives to make students learning visible. Additionally, following with Vygotsky’s zones of proximal development, it is recommended that students work in groups of two to help students learn from each other. Finally, it is hoped that if students are engaging with material that is important to them, they will continue to explore the questions after class.

Following these four guidance, I explored the Designing an Amusement Park Ride project. Students as assigned to two groups, the thrill team or the safety team. Taking on the perspective of professions in these fields they are asked to create a ride to add to an amusement park. As you make your way through the project, students are provided the opportunity to play with slopes but immediate following are asked to answer 3 to 4 multiple choice questions (reminded me of the FSA assessments). What was lacking also for me was the immediate feedback regarding my answers. For both the multiple choice and written questions I wrote nonsense answers to see what would happen and it let me progress through without correcting me. Coming back to the ideas of misconceptions, I think is a perfect example where students are answering questions using their beliefs and not being corrected along the way. I also found that there was a lack of videos. Referencing the Jasper project, one of the major positives for that project was the video components to engage students in the material in real-time. This is an adjustment I would make to this project where students are able to see a real-life example of the ride they are creating, while they are creating it.

Overall though I do believe that this could be a fantastic tool and I will be continuing to play with it. Especially to see if I can create one that works for the grade 3-5 grade range where there are currently 0 projects.

Linn, M. & Clark, D. & Slotta, J. (2002). WISE Design for Knowledge Integration, Graduate School of Education, University of California at Berkeley, 87(4), 517-538.

The Jasper Project

The Jasper Experiment, popular in the early 1900’s was a video-based learning tool that I would argue was a precursor to many of the educational goals of today. The Cognition and Technology Group at Vanderbilt University (1993) describes the experience of a child being immersed into a video and is asked to identify and create goals and subgoals to ultimately solve a presented problem. The goal of this learning experience is to “[emphasize] the importance of anchoring or situated instruction in meaningful, problem-solving context” and create classroom activities that are complex, have open-ended problem solving that connect math to other subjects and to the world outside the classroom (475, The Cognition and Technology Group at Vanderbilt University, 1993).

Like many research findings, I often question that reliability of the findings as the participants are typically in a central location. What I found very interesting about the readings this week was the article titled Using video-based anchored instruction to enhance learning: Taiwan’s experience (2000). They describe a culture that is strict on academics and typically follows the traditional, teacher-centered, memorization educational format. Using videos inspired by the Jasper series, students in Taiwan were placed into a treatment or control group. The findings ultimately appeared to be similar to that of American findings. They found that students felt more positive, interested in and less anxious towards mathematics. As well, student problem-solving skills improved significantly with anchored instruction.

These findings ultimately had me wondering, what was it about these videos that worked so well? Although the readings this week discussed some of their explanations for the effectiveness (video formatting, narrative, generative format, embedded data, problem complexity, pairs of adventures and links to curriculum), they were also written over 20 years ago. What about students today, would they feel the same connection to the videos? My answer is yes. As a teacher at an inner city school I am constantly looking for material that is accessible to my students. Many of my students are reading below grade level and when presented with written instructions become overwhelmed and shut down. I appreciate the video aspect of this tool as it provides the information in a format that I know each of my students will understand and be drawn to. Our ultimate goal is to motivate students and make them excited to learn, and I believe a tool like this would do just that.

Finally, I appreciated the discussion of assessment described by The Cognition and Technology Group at Vanderbilt University (1992). They found that student and teacher perceptions of the assessment tools originally associated with the videos was creating a negative impact on the students. I was also confused myself. Here is a fantastic tool that has been created to increase student motivation and demonstrate to them the real-world implications of mathematics, but yet we will require them to use paper-to-pencil summative assessment. In other words, it would seem that the purpose of the videos was once again to have students ready for another test. As a way to solve this concern, the researchers piloted a teleconference that had students watching videos and using descriptive, problem-solving answers to identify an expert. It ultimately had students feeling that they were learning something new and reengaged in the material.

Overall, I believe the Jasper Project is a great example of educational tools and technology that successfully implements content and technology in a way that would engage and motivate our students.

Shayla

The Cognition and Technology Group at Vanderbilt University (1992), The Jasper Series as an Example of Anchored Instruction: theory, program, description, and assessment data. Educational Psychologist, 27(3), 291-315.

The Cognition and Technology Group at Vanderbilt University (1993), The Jasper Experiment: using video to furnish real-world problem solving. The Arithmetic Teacher 40(8), 474-478.

Shyu, H. (2000), Using video-based anchored instruction to enhance learning: Taiwan’s experience. British Journal of Educational Technology, 31(1), 57-69.

PCK to TPACK

The TPACK Framework, as described by Koehler, Mishra and Cain (2013), seeks to explain how teachers understanding of Pedagogy, Content and Technology interact with one another. In 1986, Shulman introduced the idea of Pedagogical Content Knowledge (PCK) to focus on the relationship between the spheres of knowledge in hopes of balancing methods of teaching. Mishra & Koehler discuss an ideal learning environment is created when knowing what teaching approach and methods appropriately fits the content to make it comprehensible to learning (2006). Increasingly technology has become an ever present component to teaching and has been added to the original TPACK. Now it appears, teachers need to focus on what technologies can best aid in appropriate teaching methods for students to learn the content. Learning is a balance between what teachers know (Content) how teachers teach (pedagogy) and what tools (technology) is available.

Koehler, Mishra and Cain (2013) describe three approaches for the development of TPACK in the classroom.

From PCK to TPACK

Teachers draw upon their existing pedagogical content knowledge to form insights into which technologies might work well for specific learning goals.

From TPK to TPACK

Teachers build on their knowledge of technology in general to develop expertise and identify and develop specific content that benefits from it.

Developing PCK and TPACK simultaneously

Teachers gain experience and knowledge through projects that require them to define, design and refine solutions for learning problems focused on providing teachers insights into the ways technology, pedagogy and content interact.

Which of these three do you think would be most effective? Do you think there might be a smoother journey towards full integration towards TPACK? As teachers begin to experiment with technology, it is often simpler to view technology as an “add-on” to their practice. Instead, it is important to remember that focus is the connection among technology, content, and pedagogy and redesigning the classroom to simultaneously integrate each component.

In my own classroom, we are working on elements of a story with my grade 2 students. In previous years I have had students write each section of a pop-up story book as we walk through the writing process. In the end, we type out their story and glue each section on a page and students draw out the corresponding scene. Last year, once the students had created their books I had them use the ipads to 1) use a drawing app to illustrate their puppets 2) create a video of their book. The idea was to demonstrate how books can be transformed into movies. The students absolutely loved the experience and it opened up a great conversation to compare and contrast books and films.

Shayla

Koehler, M., Mishra, P. & Cain, W. What is technological pedagogical content knowledge (TPACK)?. The Journal of Education, 193(3), 13-19.