This week our goal was to create a lesson plan that connects learning theories with our Maker Kit. Right off the bat I had no problem connecting Choice Theory (and other learning theories) with my Maker Kit, Squishy Circuits. However, the biggest problem I faced was the interdisciplinary connection between science and mathematics, which seems weird because the two are so closely related. After tinkering and imaging how I could use my Maker Kit in my classroom last week, I came up with several possibilities of how I could implement Squishy Circuits into my curriculum. If I had more tools in my Maker Kit I could build a logic circuit and have students explore truth-values for conditional statements, which would be my first pick. Also, if I had a better handle on circuits, I could’ve had students explore graphing shapes and translating them on the coordinate grid, since we will re-visit coordinate geometry in the near future. I also tried to explore Graph Theory using LED lights as vertices, but I couldn’t figure out how to make it work & make sense. While I managed to come up with a game, I felt like it was a stretch and that I could play a similar game in class without circuits that was just as beneficial but took less time to set up. With that said, after reflecting on my learning process, I decided that making circuits is a lot like constructing a proof.
A mathematical proof is an argument that begins with known facts, proceeds from there through a series of logical deductions, and ends with the thing you’re trying to prove. There are several intermediate conclusions—if I do this, then I get this—that lead to the final conclusion. Similarly, when building circuits, we are given a battery pack, a light emitting diode (LED), a motor, and two buzzers (similar to the picture we receive in a geometric proof). Along with the given materials we have to make sense of circuits using with background knowledge or basic facts: conductive dough lets electricity pass through it, insulating dough does not allow electricity to pass through it, electricity is directional-the current runs from positive to negative, the LED, motor, & buzzers are directional- they have a positive side (the longer leg on the LED) and negative side (shorter leg on LED), and a circuit has to be closed (a continuous loop). From here, we have to have to use what we know to create logical steps that help us reach our conclusion or what we are trying to prove.
As I was building my first simple circuit, I realized that if I did something wrong, like put my LED in backwards (so the positive and negative leg were flipped), the LED would not light up because the circuit was not closed. Likewise, we can use unnecessary information in mathematical proofs that direct us away from our conclusion. Building a circuit is a procedural, logical process much like geometric proofs. Thus, for my activity, as an introduction to proofs I would have my students play with circuits and write a two-column proof for each of their steps towards creating a more complex circuit using the motor, several LEDS, and both buzzers. This activity seems more practical than the game I created last week and it fits better into my curriculum.
Connection to Learning Theories:
The guiding principles explored in my lesson plan [above] are driven by Diene’s Theory of Mathematics Learning, Choice Theory (Glasser), and constructivist principles. This framework allows learners to take learning from a noun to a verb. It compels learners to think critically within a metacognitive framework that requires them to formulate the problem and reflect on their thinking. Further, by blending progressive pedagogy with modern tools and resources, such as Squishy Circuits, my learners will achieve the skills they need to become innovative, original thinkers.
Writing geometric proofs is about connecting the dots. We have a starting point and an end goal, yet we somehow have to logically fill in the middle so that it gets us to the end (Ryan, 2008, p.49). It’s kind of like giving a friend directions to your house. The coolest thing about proofs is that there isn’t one correct way to reach the destination. You can have them take the back road shortcut, the city streets, or the scenic route. However, regardless of the route you give your friend, if you leave out a step or are too vague, you risk them getting lost. If you think about it, it would be nearly impossible to give someone directions to your house if you have never driven there yourself. You have to experience and understand what you are trying to communicate before you can write it in a logical organized manner. So, you have to play and experiment, make note of your observations, then order your findings logically, filling in the gaps as you go. The squishy circuit activity allows students to do just that. The lesson allows for students to experience different ways of building circuits, make conjectures and observations about how circuits behave, and then go back and write their findings in such a way that not only shows why their process is true, but also allows others to see why their process is true.
This process, in accordance with my squishy circuits lesson plan, is supported by several learning theories. In terms of learning math, Dienes’ Constructivity Principle simply states that ‘construction should always precede analysis’” (Dienes, 1969, p.32). Likewise, in the lesson with squishy circuits, learners are given “play time” to experience and observe before they begin to analyze and deduce. This process allows students to see the “big picture” in a way that fits their unique needs and abilities. Similarly, Dienes’ Theory for learning mathematics states: “When children experience a concept in more than one embodiment, they are more likely to conceive the mathematical generalization independent of the material” (Dienes & Golding, 1971, p.47, 56.). By allowing students to play with something tangible, like squishy circuits, they will be able to form an informal process for writing proofs that is unique to their personal needs. That is, the learners will gain an understanding of how to construct a proof before they actually get a formal definition of what a proof is.
In lieu of learning the learning process, Dienes’ Constructivity Principle (1969) closely aligns with Piaget’s work in that they both imply learning requires embodied experimentation, play time, group work, individual reflection, teacher as facilitator, and student responsibility/ownership. Learning is not a spectator sport. In order to gain conceptual understanding learners must experience diverse learning and make connections between old and new. By using the constructivist approach as a foundational framework in my planning, I was able to ensure that my squishy circuits lesson gave each learner the opportunity to explore and create his or her own understanding through differentiated instruction at a level that makes the content meaningful (Piaget, 1971). For example, as creative problem solvers they will make qualitative and quantitative observations as they build the circuits. Then, they will organize their observations to make sense of their findings through tables, graphs, or other visual representations, which equates to the activity where they write steps with explanation. Finally, they will make connections within their findings and to their previous knowledge by reflecting on the experience (Polya, 1957). In essence, their learning will build on what they already know and will establish new or more extensive relationships within their mental frameworks. Consequently, as learners begin to write mathematical proofs, they will make connections to their squishy circuits proof writing process and use that experience as a foundation that they can build from. This problem solving process is not only relevant to material in the mathematics classroom, it also relates to problem solving skills needed in real life situations and is highly associated with critical thinking skills.
Further, this theory suggests that if the student is given the opportunity to interact with others and question new ideas, they will move from the known to unknown. I personally experienced this during my playtime last week. I really started making progress and understanding circuits when I had my roommate and her boyfriend there to discuss ideas and complications with me. For this reason, my squishy circuits lesson allows the learners to play with the circuits and collaborate in cooperative learning groups, which will help them build of each other’s experiences. Perhaps they will make mistakes within this process, but by accommodating what they thought to be true with what they have found to be true, they are learning from their mistakes and experiences. Moreover, during the creative problem solving process (circuit making) I will act as the facilitator. I will be passive and the learners will be active. By implementing carefully designed partner activities and periods of reflection throughout my lesson, I will be able to create a classroom climate, a “math lab” if you will, that supports experimentation, discovery, and play, while providing learners with choice, which leads me to my final point (Reyes & Post, 1973).
Lastly, this learning model suggests that learners need to have choice in the process. In the squishy circuits lesson, learners will have choice to construct and play with circuits as they please, choice to write their process as it makes sense to them, and choice to create a “masterpiece” that interests them to present to their classmates. In turn, students will feel empowered and will be intrinsically motivated, which aligns with Glassner’s Choice Theory (Corey, 2012, p.402). When learners have a say in what and how they learn, they take control of their learning and achieve a sense of ownership. They will become the teacher when they explain their final product to the class. Their demonstration will show how they consolidated several concepts throughout their playtime and will convey their new understanding of the material.
By using these theories as a foundation for my lesson, I am confident I will be able to appropriately respond to the diverse, intellectual needs of the student body as well as the needs of individual learners who are culturally, socially, and economically different, too. The most rewarding thing that a lesson like this has to offer is seeing the creativity learners bring to mathematics. Processing information, making connections, reflecting, and learning through constructivism are qualities of creative problem-solving mathematicians and innovative learners and defines the educational ideology of the 21stcentury.
Corey, G. (2012). Theory and practice of group counseling. (8th ed.) [Print]. Belmont, CA : Brooks/Cole
Dienes, Z. (1969). Building up mathematics. (rev.ed.) [Print]. London: Hutchinson Educational.
Dienes, Z., & Golding, E. (1971). Approach to modern mathematics. [Print]. New York: Herder and Herder.
Piaget, J. (1971). The psychology of intelligence. [Print]. Boston: Routledge and Kegan.
Polya, M. (1957). How to solve it. (2nd Ed.). New York: Doubleday.
Reys, R. & Post, T. (1973). The mathematics laboratory: Theory to practice. [Print]. Boston: Prindle, Weber, and Schmidt.
Ryan, M. (2008). Geometry for dummies (ed. 2). [Print]. Hoboken, NJ: Wiley Publishing, Inc.
The Squishy Circuits Lesson Plan may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved.