Category Archives: e-folio

This week, I had the opportunity to try a variety of simulation software, each of which has the potential to create a dynamic, inquiry-based environment for students in science and math classrooms. The two information visualization programs that I explored in most depth were PhET Interactive Simulations (found at: https://phet.colorado.edu/), developed by the University of Colorado, and Illuminations (found at: http://illuminations.nctm.org/), developed by the National Council of Teachers of Mathematics. I chose these two programs specifically because I currently teach in a grade 4/5 split class and wanted to explore programs with simulations or games targeted at intermediate elementary students, and because I wanted to explore both a science-based as well as a math-based program.

In “A Framework for Model-Based Inquiry Through Agent-Based Programming,” Xiang and Passmore (2015) discuss a shift in the focus of science education “…from typical classroom practice that emphasizes the acquisition of content to a classroom in which students are active participants in making sense of the science they are learning” (p. 311). Today’s students are no longer passive recipients, and are instead active participants in the acquisition of knowledge. To accommodate this shift, educators today must work to develop inquiry-based learning environments which allow students to construct knowledge through questioning, collaborating, hypothesizing, and challenging prior assumptions. In designing lessons that incorporate these features, many educators are turning to model-based inquiry which may be supported through digital simulations (Xiang & Passmore, 2015).

Despite the shift in the role of the student to active participant in modern classrooms, many students continue to struggle with math- and science-based concepts presented in current curriculums. Some students arrive with pre-conceived ideas and misconceptions, some with a significant lack of experience that hinders their understanding of concepts, some with the need for adaptations to support their learning, and so on. Srinivasan, Perez, Palmer, Brooks, Wilson, & Fowler (2006) address the fact that “a learner’s success with learning new material can be described in terms of the learner’s prior knowledge, ability, and motivation (Schraw et al., 2005)” (p. 138). In a simulated learning environment, students are given an opportunity to interact with materials and situations being taught, allowing them to learn through experience and by “doing” rather than simply by reading a textbook and listening to a teacher’s lecture. Along with this, a simulated environment provides the potential to target motivational variables such as novelty, interest, and importance or value of concepts taught (Srinivasan et al., 2006).

In the case of simulation software such as PhET, students have the opportunity to interact with materials and laboratory conditions in authentic learning environments that they may not otherwise be able to experience, due to factors such as economic feasibility or safety concerns. Sound educational principles aside, Srinivasan et al., (2006) highlight the fact that “generally speaking, it is less expensive to develop a simulation than to provide real experience” (p. 137). While Srinivasan et al. referred to their study around cockpit simulations, this same concept can easily be applied to public school and university settings today. For example, I explored a simulation titled “Energy Forms and Changes” on the PhET site in depth this week and created a lesson around it. The opportunity offered to students through the use of this simulation could not be replicated otherwise in my class. The simulation offers an “Intro” simulation that allows for the heating/cooling of iron, brick, and water (with visual tracking of energy input and output), and a second more in-depth “Energy Systems” simulation that provides students with the opportunity to actually construct their own energy systems using a variety of materials. The simulations not only provide engaging learning environments for students, but they provide materials I would often not have access to, and learning environments that can be used without the extensive laboratory preparation and clean-up that would have been required had the same activities been replicated in a traditional laboratory environment (the explorations/experiments would have taken days if not weeks to complete). Finkelstein, Perkins, Adams, Kohl, & Podolefsky (2005) note that PhET simulations “…are designed to be highly interactive, engaging, and open learning environments that provide animated feedback to the user…designed to build explicit bridges between students’ everyday understanding of the world and its underlying physical principles…” (p. 2). While this reference is to PhET university physics simulations, I would argue that the principles behind it apply to all PhET simulations that I explored. Based on their research findings, Finkelstein et al., (2005) propose that “…properly designed simulations used in the right contexts can be more effective educational tools than real laboratory equipment, both in developing student facility with real equipment and at fostering student conceptual understanding” (p. 1-2).

The Illuminations website provides similar benefits for students in the form of interactive games and learning tools to support math. Students are immersed in an engaging environment that allows for digital manipulatives or games to be used to reinforce mathematical concepts taught in the classroom. Rather than having students simply complete repetitive math questions or problems in an attempt to encourage the memorization of a concept through practice, students are engaged through constructing knowledge as they actively attempt various problems and are provided with immediate feedback to support and scaffold their learning. By implementing these and other similar learning tools and games into the classroom, students are provided with learning environments and opportunities they would not have been exposed to otherwise, and with an engaging environment that promotes learning.

Interestingly, in a study they conducted, Srinivasan et al., (2006) found that university students perceived simulations as “fake” and valued “’real’ experiences” over the simulated experiences they received; “with MATLAB the students don’t have a sense of partaking in what they perceive as authentic experience. They seem to need/want authenticity to be able to make the connections the experts make with the simulation” (p. 140). I found this interesting, but wonder if it has to do with the level of learning that students are engaging in. How well a simulation is accepted may also depend on what exactly is being simulated. In the case of an airline cockpit simulation, students might feel that they are missing out on the “real” experience of actually flying a plane which could tarnish their experience of that particular learning environment. In the case of a public school-aged student, I have generally had the impression that simulated learning environments were welcome additions to a classroom, as they often expose students to learning environments that would otherwise not have been available.

While I have not used either of these programs yet with my students, I would certainly hope to use them in my classroom in the future. Both provide interactive and engaging learning environments for students that I believe help students construct their own knowledge, rather than simply absorb what they are taught by a teacher or textbook. By interacting with materials and concepts in a simulated or game-based experience that provides information visualization, students are able to see the effects of their experiments, receive immediate feedback, and then re-evaluate their conceptions/hypotheses allowing them to more forward toward learning, rather than having a teacher or textbook attempt to re-explain a concept without the hands-on learning opportunity attached.

References:

Energy forms and changes. (n.d.). Phet Interactive Simulations, University of Colorado. Retrieved from https://phet.colorado.edu/en/simulation/legacy/energy-forms-and-changes

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.

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.

Xiang, L., & Passmore, C. (2015). A framework for model-based inquiry through agent-based programming. Journal of Science Education and Technology, 24(2-3), 311-329.

Over the course of the past week, I spent a lot of time investigating and trying each of the information visualization programs presented and deciding if, or how, I could incorporate them into my classroom lessons. Admittedly, I spent the most amount of time on Phet simulations, the molecular workbench, and Geometer’s Sketchpad but I will return to investigate wiseweb, illuminations applet, and netLogo in further detail. My first impression is that all of the programs seem to be worthwhile and would enhance/extend lessons in math and science.

http://dynamicgeometry.com           http://illuminations.ntcm.org    http://phet.colorado.edu

Information visualization programs enable the student to evolve from a passive learner being fed information and expected to regurgitate it on a paper and pencil assessment to an actively engaged learner who is involved in the construction of their own knowledge. As we discovered in the various program styles introduced in Module B (T-Gem, LfU, anchored instruction, SKI/WISE) students need to identify their misconceptions, find information and test hypotheses as well as modify their thinking- which can only be accomplished if they are questioning, constructing, testing, proving and defending their theories.

Software, simulations and interactive programs are excellent educational tools. Teaching using virtual tools means every child in every class can experiment with the knowledge they have acquired. The old adage seeing is believing can be taken one step further as students do not only see in more than 2 dimensions they can alter parameters and test their hypotheses and solve for solutions. If their hypotheses were correct they have reinforced what they know, if their hypotheses were incorrect they can identify their misconceptions, modify their thinking and run further tests until they are satisfied they correctly understand the concept.

The article by Finkelstein et al (2005) “When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment” demonstrated that learning virtually is often better than regular lab experiments.  In regular chemistry classes, students have use coloured Styrofoam balls and connectors to create molecules. As the students can create just about anything they have no idea if the molecules they are creating hold up to the laws of chemistry, a computer simulation would correct any misconceptions the students had. Finklestein et al (2005) reported that “results indicate that properly designed simulations used in the right contexts can be more effective educational tools than real laboratory equipment, both in developing student facility with real equipment and at fostering student conceptual understanding (p. 2).” They further state that in an inquiry-based laboratory, students using the simulations learned more content than did students using real equipment (p. 6).

Steiff and Wilensky (2003) reported that computer-based curriculum provides an opportunity for inquiry-based chemistry lessons. “The modeling environment, connected chemistry, uses a “glass box” approach (Wilensky, 1999a) that not only enables students to visualize the molecular world but also provides them with virtually unlimited opportunities to interact with and to manipulate a simulated molecular world to gain a deeper understanding of core chemistry concepts and phenomena (p. 285)”. They further report that simulations allow students to make predictions about a concept and justify their predictions with observable outcomes (p. 286).

Although I have not used any of the highlighted math or science simulations in my classroom yet I can compare their use to my implementation of programs code.org, tynker and scratch I have used several coding programs. The one I am most successful with is Code.org. What I have learned about using this on line is that it brings coding alive through the use of block coding. Block coding takes difficult abstract concepts and chunks it together in to information the students understand and can work with. The students learning is scaffolded from the most basic coding steps to more advanced. The program provides immediate feedback to the student so they know if they are correct or not. Most also provide the students with a “safety” key so that they do not become too frustrated and quit the program. Students who are shown the answer still must go through the steps of coding the information properly before they are able to move on.

The excellent thing about today’s coding programs is that they are also geared toward the student’s interests. Students can code with princesses, Minecraft or a whole host of other themes. For the more creative student they can create their own characters and storylines to code with.

When I was a student I was taught to code on paper (sorry I tried to code on paper) but because I never understood what I was writing, I never understood how the program would react. I thought I could never understand or write code. I wrote myself off as computer illiterate. Coding programs have helped me evolve from this scared computer person to someone confident enough to teach it to her students. My students love working with these programs (every student even my some of my special needs students are great at it, they see it as a cause-effect relationship they understand).  It is vital that we start coding with our students at an early age as it has been said that coding is the language of the future. The language all workers will need to understand.

With regards to Geometer’s Sketchpad and the other math programs we looked at this week I hope to incorporate these more in my classroom lessons. I have discovered the value simulations in math to be immediate feedback to the student. In previous years when I have had students work with paper and pencil or manipulatives they often assume they are correct and consistently make the same errors, in essence reinforcing an incorrect concept. With computer simulations students are immediately shown if they are correct or not. If they are not correct they must fix their errors before they are allowed to move on. Many of the newer software companies are installing subprograms that identify specific concepts students struggle with and provide more reinforcement with those concepts.

Srinivasan et al (2006) explain the importance of a simulation being in the students current range of development and understanding. “The task must present an optimal learning challenge (Deci and Ryan, 1985). When this type of task is presented, students will perceive themselves as competent enough to be successful and enticed enough by the learning task to sustain their attention. By using appropriate assessments, we can determine reasonably successfully the ‘optimal level’ of instruction (p. 139).” What was especially interesting to note in this study was that students (the example provided was a cockpit simulator) believed simulators to be a less valuable learning experience than being in an actual cockpit, while the expert pilots found the simulator to be a valuable learning experience (p. 140). One must wonder if the basis of the student’s beliefs lie in their kinesthetic awareness of a real cockpit that an expert pilot would already have?

The articles I read on mathematics included Edens and Potter (2008), Sinclair and Bruce (2015) and Sinclair and Jackiw (2010) pertaining to Geometer’s Sketchpad, primary geometry and graphic representations in solving word problems.

To begin with the article by Sinclair and Bruce (2015) “New opportunities in geometry education at the primary school” reinforced my thinking that geometry is integral to so much of our learning they state that “geometry should be of the highest priority because it too—as a vehicle for developing spatial reasoning (p. 321)”. Yet, it is often the most overlooked and under taught mathematical unit in our classrooms. Most of my colleagues believe geometry is the unit you squeeze in in a few lessons so you can report on it. Students are often provided with basic manipulatives to “flip, slide or turn” and then draw a picture of the result.

Research by Sinclair and Bruce (2015) has shown how “new digital technologies that promote visual and kinetic interactions can help support the teaching and learning of geometry and that new technologies are already challenging assumptions about what geometry can be learned at the early primary school level (p. 324).”

I have used Geometer’s Sketchpad with my students in the past and have found it to be quite successful. Through manipulation of data points students can see how their actions influence the polygon or three-dimensional object on the screen. As stated by Sinclair and Jackiw (2010) in their chapter Modeling Practices with The Geometer’s Sketchpad the software “distinguishes between (relatively) concrete and (relatively) abstract mathematical ideas (p. 533).” I will continue to work with and investigate Geometer’s Sketchpad with my students.

Finally, the article by Edens, K., & Potter, E. (2008) “How students “unpack” the structure of a word problem: Graphic representations and problem-solving” made me stop and really investigate the way my students use visuals to explain their thinking in every subject.

“Students who used schematic visual representations were more successful problem solvers than those pictorially representing problem elements. The more “schematic-like” the visual representation, the more successful students were at problem solution (p184).”

I realize that it would likely be beneficial for me to introduce to my students the concept of schematic visuals vs pictoral visuals. Are my students drawing a picture and not really saying anything or are they using schematics to demonstrate interactions and important concepts? This idea really made me stop and think about how I have taught using visuals and that I have work to do in this area with my students.

References:

Edens, K., & Potter, E. (2008). How students “unpack” the structure of a word problem: Graphic representations and problem-solving. School Science and Mathematics, 108(5), 184-196

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.

Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM, 47(3), 319-329.

Sinclair, N., & Jackiw, N. (2010). Modeling Practices with The Geometer’s Sketchpad. In Modeling Students’ Mathematical Modeling Competencies (pp. 541-554). Springer US

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

Stieff, M., & Wilensky, U. (2003). Connected chemistry – Incorporating interactive simulations into the chemistry classroom. Journal of Science Education and Technology, 12(3),

Visual Learners versus Verbal-Logical Learners: Does it really matter which one you are?

“The Real Deal” versus “Virtual Reality”: I think there is room for both.

I have been the facilitator of gathering students together to represent the unseen phenomena of molecular movement in states of matter. Students who are “solid” stand very close together and jiggle on the spot, while the “liquid” students stand further apart and move a bit more freely. The students who represent gas find their own space and move around in comparable bliss. I have had students dramatize the story of Archimedes and the king’s golden crown, and have seen a line of students model each part of the ear as sound moves through it. These students are taking on the roles of scientific phenomena, but their role play, as Resnick and Wilensky (1998) would suggest, is merely representing the results rather than “the processes and interactions that give rise to the results” (p.168).

Traditionally role play has found itself in the arts and humanities, helping students view themselves and society through varied lenses, making connections and altering perspectives. Winn (2003) quotes Reyes and Zarama suggesting that in the sciences, too, perspectives of self can be changed. The learned distinctions can often “tell us more about ourselves than about the world we are describing” (Winn, 2003, p.19). As well, Resnick and Wilensky (1998) have found that “role-playing activities provide a framework in which learners can start to make … distinctions – learning to project only the specific parts of their own experiences that are useful for understanding other creatures and objects” (pp.168-9). Can role play in the sciences and mathematics classroom aid in growing these distinctions? In subject areas where traditionally there is one correct answer, can seemingly random and indeterminate role play help bring order and understanding to complex ideas?

Resnick and Wilensky (1998) would affirmatively attest that role play is not intended for simply representing a result, but for “developing new relations with the knowledge underlying the phenomena” (p.167). In fact, they assert that for complex and system sciences, role play is ideal for providing “a natural path for helping learners develop an understanding of the causal mechanisms at work in complex systems. By acting out the role of an individual within a system…, participants can gain an appreciation for the perspective of the individual while also gaining insights into how interactions among individuals give rise to larger patterns of behavior” (p.167). Gaining insights into how localized patterns influence larger-scale, or globalized activity, is essential in understanding the intricacies of a complex system.

The enactivism theory of cognition supports Resnick and Wilensky’s affinity for role play within the sciences and mathematics. As described by Proulx (2013): “[e]nactivism is an encompassing term given to a theory of cognition that views human knowledge and meaning-making as processes understood and theorized from a biological and evolutionary standpoint. By adopting a biological point of view on knowing, enactivism considers the organism as interacting with/in an environment” (p.313). As the organism and environment interact, both change and adapt in response to the interaction, making them even more compatible. This evolution of structure is referred to as coupling (Proulx, 2013). Learning through enactivism is neither simple nor linear, but rather complex and undetermined. Using role play to understand mathematics and complex and science systems takes the student through an evolutionary process of change. The student takes on a role, interacting with the problems (environment) presented, and through this interaction poses new problems and pathways of solution. Along the way, the student finds their initial role is changing too, in order to adapt to the changing environment. 

Interestingly, the chaos theory of instructional design also recognizes the value of instruction and learning that is evolutionary in nature (You, 1993). Similarly to Resnick and Wilensky, the chaos theory allows for patterns and order to emerge from seemingly randomness and chaos. You (1993) states that central to the chaos theory is “[t]he discovery that hidden within the unpredictability of disorderly phenomena are deep structures of order” (p.18). Quoting from Hayles (1990, 1991), the characteristics of the chaos theory are described with such phrases as a pattern of order within disorder; chaos is the precursor and partner to order rather than the opposite; and chaos is paradoxically locally random, but stable within a global pattern (You, 1993).

To bring this back to role play in mathematics and sciences, there is a need to recognize that complex ideas can be defined and understood through role play scenarios and interactions whether technology-based or non-technology-based. Through role play, localized complexities can be more clearly defined through continual problem solving and problem posing that allow the learner to begin to see and interpret patterns that emerge. As Proulx (2013) states, “The problems that we encounter and the questions that we undertake are thus as much a part of us as they are part of the environment; they emerge from our interaction with it” (p.315).  Perhaps by opening the world of role play to mathematics and science students, we will see more students acting like Barbara McClintock, a Nobel-winning biologist who attributes “her greatest discoveries to the fact that she had a “feeling for the organism” and was able to imagine herself as one of the genes within the corn (Keller, 1983)” (Resnick & Wilensky, 1998, p.168). Perhaps McClintock’s experience is a call for educators to consider further the possibilities for when students are handed permission to relate and interact through imagination, and hence are given opportunity to experience phenomena.

The possible’s slow fuse is lit by the imagination. ~ Emily Dickinson

Resnick, M. & Wilensky, U. (1998) Diving into complexity: Developing probabilistic decentralized thinking through role-playing activities, Journal of the Learning Sciences, 7(2), 153-172. DOI: 10.1207/s15327809jls0702_1

Proulx, J. (2013). Mental mathematics, emergence of strategies, and the enactivist theory of cognition. Educational Studies in Mathematics, 84, 309-328.

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

You, Y. (1993). What can we learn from the chaos theory: An alternative approach to instructional system design. Educational Technology Research and Development 41(3), 17-32. Retrieved from http://www.jstor.org/stable/30218385

As a kinesiologist, I always look for ways to connect learning to movement. This week’s readings were right up my alley. Especially considering I had just tried Leap Motion technology and a 3D geometry activity with my class.

The question:

How could you use what is developed in these studies to design learning experiences for younger learners that incorporates perception/motion activity and digital technologies? What would younger children learn through this TELE (technology-enhanced learning experience)? Fit perfectly with what I was working on.

In the readings for week 11 a good foundation for using motion and perception with teaching in math was laid out. For example, Winn (2003) stated “once we start to think of cognition as the interaction between a person and their environment, it is necessary to consider how that interaction occurs. This, in turn, requires the consideration of how our physical bodies serve to externalize the activities of our physical brains in order to connect cognitive activity to the environment (p. 93).” Students need to use their bodies to interact with the environment and the concept they are trying to understand. Geometry, including 3D geometry is an excellent example of this. If students do not get a chance to understand how objects move in 3-dimensional space how can they be expected to learn this on their own? Looking at a rectangular prism on paper is much different than holding one in your hand and manipulating it by sliding, flipping it or rotating in in real space.

As modules continue students will scaffold their learning from concrete to abstract and then consolidate their actions into gestures so that deeper learning, as well as easier transfer and recall will occur. Novak et al. (2014) stated that “gesture promotes transfer of knowledge better than action, and suggest that the beneficial effects gesture has on learning may reside in the features that differentiate it from action (p. 445).” Lindgren et al (2013) reported “there is increasing evidence that body movement, such as gesture, can serve as a “cross-modal prime” to facilitate the retrieval of mental or lexical items (p. 447). Finally, Pouw et al (2014) found that:

1. Under certain conditions, perceptual and interactive richness can alleviate cognitive load imposed on working memory by effectively embedding the learner’s cognitive activity in the environment (Embedded Cognition claim).
2. Transfer of learning from manipulatives does not necessarily involve a change in representation from concrete to symbolic. Rather, learning from manipulatives often involves internalizing sensorimotor routines that draw on the perceptual and interactive richness of manipulatives (Embodied Cognition claim) (p. 53)

As a kinesiologist I have always benefitted from doing rather than imagining. My body is the instrument I use to understand my world and my place in it. As an educator, I want my students to rely on their bodies as a learning tool. If the use of manipulatives enriched learning, imagine the leaps and bounds that could be made if at an early age students kinesthetically understood what these terms implied? For example, with students as early as kindergarten and continued through primary education what if we take geometry on a cross curricular journey into the gym.

Using the technology of a white board or projector the teacher could introduce the idea of translations (sliding across a surface), rotations (spinning their bodies right, left, forward, backward) and flipping an object in the same manner. Students could use their bodies to change their shape, curl up into a ball, spread out into a star fish. Once the idea of the movement in three D space has been introduced large scale objects could be moved, such as yoga balls, large cardboard boxes, large cylinders. As students become more comfortable with the movement of the object the size of the object can be diminished until it fits in their hand. A final step would be to use technology (with programs such as the Leap motion 3d geometry app) to have students manipulate virtual objects.  Following these steps would build and reinforce neural pathways and eventually students (as they mature) would be able to use this information to try and do the manipulation mentally.

Kim et al (2011) noticed that students in their study often naturally gravitated to using their bodies to mimic actions. They state “her thinking develops in and through her gestures, and her gestures further develop her thinking. Her gestures constitute the thinking with and about shapes and motion (p. 230).”

They found firstly “that children’s bodies (bodily orientations and gestures) constitute an integral part of knowing, thinking, and learning supporting the appropriate of geometrical concepts before the age thought possible (p. 233).” Secondly, the children’s co-emerging gestures allowed new concepts to be enacted for themselves and others and, thereby, for new concepts to become reflexive objects available to individual and collective inspection (p. 233).”

If students benefitted from using their bodies while seated in a classroom imagine the possibilities of using their bodies in the 3D space of a gymnasium.

Kim et al (2011) conclude that “as children think, develop, and express knowledge through their bodies, their bodily engagement needs to be realized as integral to student learning. Their bodies are necessarily engaged in coping with the abstractness of knowledge. Their bodies embody the knowledge of science and mathematics and become part of knowing itself (p. 235).”

As I noticed when my students tried the Leap Motion 3D geometry technology and app in the classroom (in groups) they were moving their bodies through space, helping each other visualize the end result of a manipulation in space. The collaboration seemed to help them solve problems and persevere more than when students worked alone. This coincides with the research by Hwang et al. (2013) that students were more successful when collaborating using new technology (p 318).

Finally, by observing students at each of the various steps outlined above there would ample opportunity for the teacher to evaluate or assess the students’ knowledge in a new way. Bodily movement and the manipulation of objects using technology can be assessed over a paper pencil test. This unit would also provide an excellent way for students to document their growth in the math using a digital portfolio, digital story or digital movie or interview. Can’t wait to give this a try.

Catherine

References:

Hwang, W. Y., & Hu, S. S. (2013). Analysis of peer learning behaviors using multiple representations in virtual reality and their impacts on geometry problem solving. Computers & Education, 62, 308-319.

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.

Lindgren, R., & Johnson-Glenberg, M. (2013). Emboldened by embodiment: Six precepts for research on embodied learning and mixed reality. Educational Researcher, 42(8), 445-452.

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.

Pouw, W. T., Van Gog, T., & Paas, F. (2014). An embedded and embodied cognition review of instructional manipulatives. Educational Psychology Review, 26(1), 51-72.

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