CEP 820: Reflecting Thoughts on Building an Online Course Module

My goal was to create a fully online learning environment that afforded the same unique learning experiences and opportunities as my traditional math classroom, which proved to be a lot more difficult than I imaged.

The design decisions within this course changed several times. When I first began developing my online course, I had the idea that I would just upload content and make it available for my students to access as they needed. Sort of like I do now for my face-to-face classroom. I hadn’t really considered the organization and I definitely didn’t consider the factors that go into policy and practice. As a traditional classroom teacher, the specifics of policy and practice are developed and modeled much differently; they occur much more naturally. However, after reading through various lectures and participating in is several “play” and “design” activities, I realized that developing an effective online course model would require a lot more than I had initially thought. It would require me to be intentional not only in my design choices but also in my instructional choices. Specifically, in order to create an online learning environment that is conducive to learning, my instructional and design choices would have to be much more explicit. I would actually have to think about the learning progression and how my online classroom would run, opposed to the natural progression that occurs in the classroom.

Similarly, the style of teaching has to change with an online course. By reflecting on my own online learning experiences and through the assignments in CEP 820 (assigned lectures, resources, and tasks) I began to realize just how naïve my initial thoughts were about online course development. Additionally, I was sort of disappointed in myself for forgetting about my own powerful online learning experiences and how they helped me develop as a learner and teacher…I should have known that it would require more than uploading content to create an effective online module. Let me elaborate. I would say I am not a traditional mathematics teacher. I use a much more progressive, creative approach. You see, I have a particular passion for online learning, especially when it comes to math. As far back as I can remember, math has always been a struggle; it never came easy for me. In fact, I was actually pretty bad at it! I wanted nothing to do with it after high school. However, as a freshman in college I took an online math course and REALLY learned math for the first time. It was the most rewarding experience; it is the reason I became a teacher. I loved being able to rewind the video- something you can’t do to a teacher- and learn at my own pace. After that I took several other math courses using video instruction–all the way up to Calculus II. I also took four other courses using online instruction–all of which I excelled in. With that established, you should also know that online learning is really the driving force as to why I became a teacher; it changed the way I felt about learning and helped me realize I was capable of understanding math. Consequently, technology integration has shaped my classroom environment and my teaching methods.

Through this reflective process, I was able to refocus and refine my online learning design to better align with my instructional goals. That is, I wanted my online course to encompass similar design features, tools, and supports that afforded me with such positive, powerful learning experiences. Additionally, I wanted to provide my learners with the opportunity to engage in the type of learning that fits them best, using tools and resources that support their unique talents and abilities. Because I know first hand the effectiveness of carefully designed and operated online courses, I felt a lot of pressure to ensure my online course would encompass the design features and tools necessary to make learning possible for ALL learners, including learners who struggle with math, much like I used to. Thus, I concluded that organization was key to producing a successful online course. As an online learner in the MAET program, I have particularly enjoyed the overall design and setup of my graduate school classes. Consequently, I modeled a similar structure in my online course. This model allowed me to scaffold instruction and learning by delivering lesson content in chunks and it provided consistency in content delivery.

After I had mastered content delivery and organization, I was able to tackle differentiated instruction, unique assessment opportunities, collaborative workspaces, and timely feedback amongst other things. Rather than dispensing knowledge and information as I had initially thought I would in my online course, I was able to optimize learning through scaffolded instruction, tools and supports and by creating differentiated, unique opportunities for learners to interact with the course content and each other using interactive multimedia and discussion forums stimulating conversation while providing direct, immediate feedback. Through the differentiated tasks, “quick checks,” and feedback, I was able to inform teaching and learning. Also, after reviewing the Universal Design for Learning guidelines, I refined and improved my content delivery and organization to ensure I was providing all learners with the opportunity to engage in the type of learning that fit them best, using tools and resources that best supported their unique talents and abilities, which I was able to identify through the task design and feedback. Specifically, I focused on providing multiple representations of content and differentiated delivery approaches in addition to unique assessment opportunities, affording all students with the opportunity to demonstrate learning. This is shown in module six in my online course where the learners are provided with additional instructional videos, multiple representations of lesson material, interactive applets, practice problems and activities of varied levels, and objective (skill and performance) based assessments.

Taken together, both organization and differentiation of content led me to my ultimate CMS choice, which is Haiku Learning; however, as I will explain below, it wasn’t an easy process. The goal for my fully online math course was to develop an individualized and differentiated approach for students learning online, and I was hoping to discover a CMS platform that would encompass my instruction, design and feedback ideals through features built right into the framework. As I will elaborate on below, the biggest issue I ran into during my CMS selection was that I would focus on one aspect of something I wanted my online course to encompass, and I would focus on that only, neglecting the other must haves I identified. So, for example, if I liked the organization and grade book feature, I would ignore the design capabilities…typically finding out too late that the platform didn’t accommodate the type of content delivery I needed it to.

When it came time to choosing our Course Management System (CMS), there were several aspects that I focused on, such as but not limited to: organization of information/course design, usability, built in grade book, collaborative work spaces, built in assessment tools, assignment collection features, and the ability to embed outside content/multimedia. So, during a CMS comparison task, I focused on checking whether or not different management systems afforded the design, features and tools I was looking for. After the CMS comparison activity I selected CourseSites because it aligned the most with the type of platform I was looking to use. However, it didn’t take me long to realize that I didn’t spend enough time “playing” during the CMS comparison activity, rather I spent most of the time reading about features and clicking to see how they would appear on a course page. So, despite the fact that CourseSites checked out on paper, it didn’t check out during the construction stage, which I elaborate on here. Because I planned to embed multimedia and interactive applets to make certain online learning experiences more tangible, I made the quick decision to switch over to Weebly for Education. This was a safe choice because I have used Weebly throughout my teaching profession. However, after spending quite a bit of time designing my online course on Weebly and uploading content, I realized that what I was gaining in freedom of design, I was giving up in organizational structure. Trying to set up links and hide content pages proved to be too much of a hassle; disorganization and confusion was inevitable. So while Weebly meets my more traditional needs as a face-to-face instructor, I realized that it was definitely not working as a platform for my online math course. With no idea what to do next, I headed back to the drawing block (AKA: the CEP 820 showcase of student work). However, through my platform-choice-failures, I was able to develop a clearer understanding of the CMS features I could not work without. That is, I had to figure out which CMS platform could offer me structure and organization similar to that of CourseSites in addition to the design freedoms, such as the ability to embed multimedia, afforded by Weebly for Education. Having established a more explicit design agenda, it didn’t take me long to realize that Haiku Learning was the obvious CMS choice for me, which surprisingly, wasn’t one I reviewed earlier in the course.

Looking back, if I were to offer up any advice to future online course developers, it would be to spend time actually “playing” & building during the CMS comparison activity, rather than researching and window shopping. That is, any car salesman could show you a beautiful car and hand you a printout of the car’s history and features, but chances are you wouldn’t buy it without test-driving it at least once, right? What I mean is, to really understand if the CMS’s tools and features will align with your course vision, you need to test them out. Reading about them in FAQ section isn’t enough, even if they show you pictures J Trust me when I say this: you will save yourself time and trouble in the long run if you spend adequate time properly playing and experimenting with the different course management systems upfront.

Having completed CEP 820, I have a much better understanding of how to effectively design and inform online learning. Through this course, I was able to reconnect with personal learning experiences that I had forgotten about to create an effective online course module that I can build and expand on in the future.

CEP 813: CMS Assessment Design with Haiku Learning

Assessments should be used as a way to gauge where students are in their learning and the feedback from the assessments should inform both instruction and learning. However, I think that more often than not educators are forced to give assessments that generally don’t align with their instructional style and fail to provide insightful feedback. Sometimes I feel like assessments are used just to provide some sort of data to parents…to communicate a grade in a way that parents understand, even if it doesn’t serve a purpose for improving teaching and learning. For me, I didn’t understand math until I was in college and was taught to reflect on my learning rather than erase mistakes. Based on my personal experiences, for my online math assessment design, I included both traditional assessment measures and nontraditional assessment measures such as, reflective think-aloud, investigations that require problem solving, reasoning, and proof, and collaborative workspaces.

Through both my screencast and this post I am going to tell you about the assessment I created for 8th grade math students enrolled in a fully online math class using Haiku Learning.

CMS: Haiku Learning

Log-in Link to Haiku Learning Math 8 Course, or you can self enroll using this link and by entering 527L3. Keep in mind, this fully online 8th grade math course is something that I am still designing and working on. It is a perpetual work in progress.

Subject Matter: 8th Grade Math: Pythagorean Theorem Unit (Geometry)

Assessment Location: Unit 6: Pythagorean Theorem; Lesson 1: Assess.

Age/Grade level: 8th Grade

Role of intended student: 8th Grade Math Student

Type of course: Fully Online

CMS SCREENCAST LINK

CMS ASSESSMENT DESIGN/CREATION RATIONALE:

There are several reasons why I chose to use Haiku Learning for my CMS assessment design. First, haiku learning is both effective and efficient: the design is clean, user-friendly, and easy to manage from an instructor and student’s perspective. Haiku Learning also has gradebook and multiple assessment features built into the site making it not only a great platform to teach learn and assess but also to communicate progress and proficiency accurately and in a timely manner to both parents and students.

Additionally, Haiku learning is extremely efficient from an instructors perspective as content is easily embedded and uploaded, as you can see in the videos and the multiple-choice assessment on the site. Moreover, for both teachers and students, there is an equation editor available any time you choose to type, which is key for math students especially in an online environment. Lastly, the calendar, announcements, discussion forum and Dropbox are just a few great features designed in the CMS’s infrastructure that make assigning, collecting and assessing a well-organized process.

For this particular task, the assessments I created are designed to measure whether learners have reached the desired learning outcomes at the end of the first lesson of the Pythagorean theorem unit. Since assessment should inform both teaching and learning, I will show you how the lesson design, activities, and tasks align with the assessment tasks, goals, and standards.

As shown in the screencast, the lesson and assessments are aligned with Common Core State Standards for 8th Grade Geometry and the Common Core State Standards for Mathematical Practice. Additionally, I explain how the assessment tools I have created will be used to measure proficiency regarding the basics of the Pythagorean theorem: what it is; why it makes sense; and how to use it.

The Pythagorean theorem is one of the main topics covered in an 8th grade mathematics geometry unit, which is also a standard students will be expected to further develop in both high school geometry and trigonometry. Furthermore, the Pythagorean Theorem is commonly present on standardized assessments such as the M-Step and ACT, and in the ever changing world of standardized assessments, the Pythagorean Theorem and its applications have withstood the test of time, making it a key standard for secondary math learners.

Specifically, for this task, I created three different assessments. For the first assessment, I used the built in assessment creation tool in Haiku Learning. This tool, the equation editor, automatic feedback, and direct link to the gradebook made Haiku learning an easy choice for this assessment. The last two assessments utilize the discussion board tool built in Haiku learning. Again, the discussion board tool has a built in equation editor and also allows students to upload pictures and documents to their posts. Perhaps the most impressive tool, though, is the built in rubric creation tool that links rubrics directly to assessments, discussion forums, and the gradebook, making Haiku learning the best choice for all three different types of assessments I created. In addition to those unique features, the discussion board assessment tool allows for collaboration and stimulates conversation.

These three different assessment tasks are designed to give all learners the opportunity to show they have mastered the skills in the first lesson. By differentiating the instruction and assessments, I believe I will be able to more accurately gauge what students truly know in addition to identifying misconceptions. That is, the multiple choice assessment allows me to check their computation and retention, while the metacognitive problem writing and reflective proof re creation assessments allow me to assess transfer, or each learners ability to apply their learning to new scenarios, in addition to each learners ability to consolidate and connect new learning with old. For example, in the Starbursts Re-Creation Proof assessment, I ask learners to consider using half of a Cheez-It on one side of their right triangle. By posing that question, I will be able to see if learners have made the connection between irrational numbers and the Pythagorean Theorem. Additionally, by having students write and solve their own problems dealing with the Pythagorean Theorem, I can ensure that students understand both the math content and vocabulary associated with the Pythagorean Theorem and how to apply that to new real world contexts.

Taken together, these assessments will accurately and effectively measure whether or not learners understand what the Pythagorean Theorem is, when to use the Pythagorean Theorem, and how to use the Pythagorean Theorem.

REFLECTION ON ASSESSMENT DESIGN AND IMPROVED LEARNING OUTCOMES:

Moreover, after reflecting on this weeks task of using a Content Management System to create an assessment, I feel as though the assessments I have designed align with my instructional design, which I hope stimulates learners’ curiosity, engages them in differentiated tasks, and intrinsically motivates them. By creating a collaborative workspace, students are able to ask questions and participate in interactions between one another.

I’ve also included traditional quizzes and non-traditional performance tasks. In addition to traditional assessments, which students may try to cheat on but I feel are still necessary, the performance tasks allow students to demonstrate what they know and evaluate their own learning through reflection. I tried to balance the types of assessments so that they scaffold learning but also inform teaching and learning in different capacities. For example, the results from a multiple-choice test provide much different information on learners’ understanding than the evidence revealed through reflective posts or performance tasks. I don’t think that one form of assessment provides an accurate measure of students understanding, so I included various forms that allow me to gauge where my students are at and how they are progressing using different approaches. Through this process, students will receive feedback regularly from their peers and me.

  • What went into your choices as you focused on certain aspects of your assessments?   While designing my online math assessments I decided I would take what I have learned thus far in the MAET program about online learning, how we learn and instructional design and combine those factors with the format and design of many of my MAET classes, which are also fully online. In addition to the design, I tried to focus on efficient, yet differentiated presentations of lesson content and assessments that aligned accordingly. This task has proved to be harder than I initially thought it would be. I tried to focus on including both traditional and nontraditional assessment methods that allow learners to demonstrate what they know. So, in addition to multiple-choice-like assessments, I made it a priority to implement performance based assessments, reflective assessments, and collaborative assessments. Regardless of the assessment type, I also focused on providing feedback within and throughout the lessons and assessments. For example, responding to reflective posts or setting up quizzes so learners receive automatic feedback based on their correct/incorrect answers.
  • How will your assessment of your students be a tool to grow your students’ learning? The assessments shown in the screencast are designed to inform teaching and learning. Through immediate feedback on lesson quizzes students are able to identify their strengths and weaknesses. Similarly, that data provides insight to me as their instructor on which areas I need to go back and re-teach. Moreover, the assessments I implemented in each lesson are designed to stimulate collaboration and reflection. This allows me to assess learners understanding on an individual level and within a community. For example, in the third assessment, students are recreating a proof using Cheez-It snacks and posting their findings to the class discussion. They are also writing their own real world problems and providing insightful feedback to their classmates. Through differentiated assessments learners are receiving feedback from multiple sources and are making adjustments in their learning as they progress, which ultimately leads to personal growth. In fact, learners will not only grow by completing the assessment tasks, they will also grow by reading and providing feedback to their classmates and reflecting on the process. Through this process, by providing multiple different methods of assessment in each lesson, I hope that learners are appropriately challenged and stimulated and if they aren’t that the data collected from the various assessments informs my instruction and allows me to make changes.
  • How will students be involved in the assessment and evaluation process? The way students are involved in the assessment and evaluation process differs based on the assessment design. For example, in reflective assessments, students will receive personal one-on-one feedback from me, sort of like the feedback we receive in our portfolio for CEP 813. Based on my feedback and questions, learners are able to modify and edit their posts and assignments. Moreover, in collaborative assessments, students are involved not only by providing feedback to their peers, but also by responding to the feedback they receive from their peers and me. In additional to reflective and written assessments, students are involved in their lesson assessment quizzes based on how they respond to their immediate feedback and score. They should accommodate their study habits based on their performance scores so they can make improvements by the time they reach the unit summative assessment.

CEP 813 – Module 1 – Annotated Assessment/Evaluation Exemplar

In Module 1: Foundations of Assessment and Evaluation, we were asked to take a critical look at the design of a typical classroom assessment we have used in our teaching profession. The assessment I am analyzing was designed as a summative assessment for an 8th grade math unit on the Pythagorean Theorem. The formatting/sizing of the questions may look funky because I built the test on Schoolnet, an online assessment and reporting system we use in my school district, so it is a digital assessment that I downloaded into a PDF version so you all could see.

Underneath the assessment shown below, you will find my critical analysis of the assessment.

Critical Analysis of Assessment Design:

a) How would I describe the design of this assessment? The assessment was designed as a summative (end of chapter test) for an 8th grade math unit on the Pythagorean Theorem. The assessment includes multiple choice, gridded (type in the number), and open response questions. The assessment is also designed to have at least a two question spread for each of the six skills (3 standards) I assessed.

b) What is the purpose of the assessment? Since it is a summative assessment, it is designed to be evaluative rather than diagnose. That is, the purpose of this assessment is to determine levels of understanding and achievement for each learner and convey that information to them in a transparent way, evaluate the effectiveness of my instruction and assessment design for the unit and make changes accordingly, measure each learners’ progress/improvement on each learning goal (skill in terms of growth and proficiency levels, and make decisions regarding students that need re-teaching and re-assessment before moving onto the next unit. Specifically, the purpose of this assessment is to convey the growth and mastery level of each skill for each student in a transparent way and report/record the achievement levels. The specific learning goals/standards are shown in part (c).

c) How does this assessment align, if at all, with the curriculum standards that guide my professional practice?  The assessment aligns with the Common Core State Standards for 8th Grade Mathematics. There are three standards that align with the unit, which are broken down further into six skills that can be seen in the document shown beneath the standards.

CCSS.Math.Content.8.G.B: Understand and apply the Pythagorean Theorem.

  • MATH.CONTENT.8.G.B.6: Explain a proof of the Pythagorean Theorem and its converse.
  • Skills for standard:
  • MATH.CONTENT.8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • MATH.CONTENT.8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

d) What information will this assessment give me about each student? This summative assessment will tell me each students scale score for each skill assessed this unit. That is, I will know the level of understanding each student has in relation to each skill I assessed. I will also look for growth shown throughout the unit. Between smaller assessments covering each individual skill (concept quizzes) and formative assessments in class, the students and I have been tracking their progression throughout the unit. The summative assessment should reveal growth for each student from where they were at the start of the unit, where they were as we progressed in the unit, and where they were when they finished the unit.

e) How do I intend to use the information provided by this assessment? I use the information on summative assessments to tell me which students need to stay after for re-teaching sessions and a re-assessment. Students only re-assess on skills they aren’t proficient in, so they aren’t necessarily retaking the entire assessment. The nice thing about having concept quizzes and formative assessments throughout the unit is that most of the misconceptions and/or gaps in understanding have been addressed before we get to the summative assessment. Like I said previously, the summative assessment is evaluative rather than diagnostic. I typically have a good idea on what students know and how they are going to do before they take the summative assessment. I think the students would agree and say they also have a pretty good idea of how they will perform on the summative assessment. I use the findings from the summative assessment to report progress and achievement to students/parents in a transparent way. Further, I use the data collected on summative assessments to analyze, modify, and improve the assessment. Sometimes the data reveals that I may have a confusing or just plain bad question that needs to be thrown out or rewritten, so I use those findings to evaluate the effectiveness of my assessment, too.

f) What assumptions have I made about whether this assessment will, in fact, give me the information I need about the students who do it? I have assumed that this assessment will reveal accurate results regarding each student’s level of proficiency in each of the six skills. I have assumed that my questions are transparent, accurate, effective, and do not need to be modified. I have assumed that the scale scores I have established are accurate, fair, and represent growth and achievement levels accurately for each learner & each skill. I have assumed that students who practiced the skills and made improvements based on the feedback they received throughout the unit will continue to improve and will show levels of mastery for each skill being assessed. Contrastingly, students who have continuously not completed practice sets, concept quizzes, or participated in formative assessments in class assessments will lack growth in most areas and will not show levels of proficiency for most, if not all, of the skills being assessed. I have assumed that this assessment design will accurately assess all of the skills we have covered this unit. Lastly, I have assumed that the assessment can be easily broken down into the different skills being assessed to show where students need improvement and where they are proficient.

g) What skills have I assumed students have that will enable them to complete this assignment? I have assumed that students can read and work technology, since the assessment is online. I have also assumed that they understand how to use the online assessment and the embedded tools. In relation to the content, I have assumed that, when given formulas, students can perform mathematical operations to either simplify or solve equations depending on the scenario… although I am not sure I would say I assumed that information since this is the summative assessment and I typically have a pretty good understanding of what students can and cannot do mathematically at this point.

h) For whom would this assessment prove difficult? Why?  This assessment will be difficult for students who struggle with application of mathematical concepts and theorems in real world and mathematical scenarios. Moreover, students that struggle with relating mathematical formulas to word scenarios will struggle as several questions require deconstructing text and applying multistep mathematical computations. Students who struggle with graphing will also struggle with the skills that requiring graphing distances in the coordinate plane. Further, students who have not practiced the skills throughout the unit or worked towards improvement based on the feedback they received throughout the unit will also struggle on the summative assessment.

i) Based on my readings this week, are there ways that I can imagine re-designing this assessment so that it’s better in some way? Explain your rationale and justification for your re-design idea(s). I think there is always room for improvement, and after this weeks readings, I definitely think this assessment should be re-imagined and structured to motivate more students to want to do well rather than complete it as a means to an end. I think including a reflective piece or maybe a short answer portion where students write their own problem would be one way I could attempt to improve the design and learner motivation. Another idea would be to include some sort of project or performance task where learners complete the proof of the Pythagorean Theorem using manipulatives. Although, that is already a formative task we do earlier in the unit. I do think that some sort of hands on task would be a way to reach learners who are better at orally explaining what they know or physically showing what they know.

I think that the assessment I made is designed well in relation to the content and skills I want to assess and in terms of the information I hope to get form the assessment. Prior to this point there have been several formative assessments embedded within instruction and feedback has been provided several times daily, so my students have been able to diagnose weak areas and improve them before the summative. Perhaps, instead of giving the assessment online with all of the skills on one test, I could break the summative into six separate assessments so the learner has a clearer understanding of what skill is being assessed, although, reasoning to decide what the actual problem is or what the question is asking and then deciding how to complete the task is an important feature of the design of the summative test that covers all six skills. I think that separating the skills into separate assessments may trivialize the assessment all together. Part of what I am looking for is whether students know when to apply the Pythagorean Theorem or its Converse and whether or not they know which method, formula, and/or theorem they need to complete real world and mathematical tasks.

Maker Kit Lesson Plan

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.

References

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.