Last year when the world had to lock down because of the global pandemic I know a lot of teachers felt extremely overwhelmed and concerned as to how to help students engage with math digitally, and I did too, but I also love a challenge because I believe they help you grow as a person and educator. Last year I tried a lot of different technologies to help my students engage with math in a meaningful way and once I found a few I liked I stuck with those. However, after a year of playing with a bunch of different technologies - desmos, FlipGrid, PearDeck, Kami, GeoGebra, the Google suite, quizlet, blooket, etc - I now have so many tools to pick from if I want to present material in person in a new or different way. FlipGrid in particular surprised me in its usefulness in a math classroom. FlipGrid integrates with a lot of platforms, so I was easily able to link it to my google classroom, and it allows students to post short videos to share out with the entire class, or only me. I only used FlipGrid once during our virtual school year last year, in part because my first and only attempt I felt was a bit of a failure. I wanted to hear my students talking about math, so I came up with five different questions that they had to answer out loud and they could show their work on a piece of paper in the video as well. And while my students did an excellent job and it was wonderful to see and hear my students talking about math, it was a bit uninspired and overwhelming of a task for some. Since then, and after brainstorming with my amazing classmates in my MSU CEP 805 course, I have had so many new ideas for how to implement FlipGrid in the classroom and I have even put them to use a few times this year. I had my algebra 1 students create their own ‘graphing stories’ videos and then watch their classmates and graph them on paper. Feel free to use this activity that I created for my students, inspired by the website - graphingstories.com For our upcoming surface area and volume unit in geometry I will have students find objects at home to take pictures or videos of with a ruler so that we can find their measurements, or at least talk about how their measurements might be similar, different, or related. And finally a project I am working on currently for my algebra 2 students is one in which I will have them take video of rolling a pair of dice a number of times, pulling out a card from a standard deck a number of times, pulling candy out of a bag a number of times, etc. to simulate experimental probability that we can then watch everyone in class do this and find those probabilities. If you have other suggestions on how to implement FlipGrid in a math classroom, please comment below! While all these new ideas are exciting and fun to try, there is always the worry that a student may not have stable internet to do this at home, or the home life to feel safe in posting a video like this. You may have students who do not attend to the task at hand, or do not feel comfortable being on camera. Luckily building up trust in your classroom can alleviate some of these concerns and FlipGrid has emojis you can put over faces, or a blur feature if you do not want to be on camera. And luckily my school is fortunate enough to be one-to-one so each student has a Chromebook with a webcam, so as long as I provide some class time to complete the task usually it can get done. Resources:
Misura, M. (2021, October 10). Graphing Stories. [Image].
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Something that I have struggled with throughout the course of my teaching career so far is how to accurately and fairly assess students' learning. In the traditional sense from what I have seen as a student, teacher, and heard from my colleagues who have been doing this longer than I have, the way to assess in a high school math classroom is half way through the chapter you take a quiz and at the end you take a test. These should never be multiple choice and students should absolutely use a calculator (or with specific skills they absolutely should NOT use a calculator). Students should always have a significant amount of homework to practice skills on their own daily and if they have questions they are responsible for asking for clarification during class, if time allows or if not, on their own time.
Ok, I’m exaggerating a bit - but not much! I am a very competitive person so proving myself on a test was always fun for me - but I know that that is not how everyone sees a test and research has taught us that not all students can perform well on these traditional style testing methods. You tend to teach how you were taught or how you best learn, so when I was first starting out as a teacher I did exactly the formula above (lots of homework, mid-chapter quiz, test). But after years of seeing students struggle to manage the workload, be successful on a traditional style test, and overall see the joy leave the room as I say ‘take everything aside from a pencil off your desk,' I had to start thinking of other ways to to assess my students learning for their sanity and my own.
This is something I am still struggling with year after year and this week I tried to put some work in to improve my Knowledge of Content and Students in regards to assessment (Hill & Ball 2009). Overall the goal is have students gain mastery and deep understanding of the content and one of the best ways to ensure this is happening is to use feedback to drive instruction (Humes 2021). How we go about doing this has been argued many different ways and managing thirty plus students per class period increases the difficulty of this as well. However, over the years I have introduced labs, projects, reduced the amount of homework I give, and have students take daily check in ‘quizzes’ to give me a guide as to how they are progressing through a unit.
One unit in geometry in particular lends itself to assessing outside the box in an obvious way to me - whenever we approached the idea of area, surface area, and volume I can think of numerous projects that students could engage with and actually talk about measurement in a real way. Bringing objects from home to physically measure and talk about, or finding things in the school, or creating origami to then find the surface area or volume helps to bring math and measurement to life. What I never had considered in terms of measurement, until diving deeper into the Common Core State Standards, is that probability is the core focus of measurement in the high school standards. Perhaps now is the time to admit another one of my weaknesses in my Specialized Content Knowledge area and give myself another perfect opportunity to increase that knowledge for the benefit of myself and my students (Hill & Ball 2009).
Resources:
Hill, H., & Ball, D. L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68–71. Humes, A. (2021). Formative assessment and technology in the mathematics classroom. [Master's thesis, Northwestern College]. NWCommons. Thinking about geometry and my tumultuous relationship with it these past few weeks has made me come to realize how much I have grown to love the subject and the added challenge it seems to come with when teaching it to high school students who over the years have heard from upperclassmen that ‘proofs suck’ and ‘geometry is awful’. And while some topics are still a struggle for me to get across to my students, I love the challenge of finding new activities to bring to them to help them appreciate it like I do. One activity I love is at the beginning of our quadrilaterals unit I always have my students begin by creating two columns split 3 times to create 8 boxes on their paper. Then I tell them to fill one box with the name of one quadrilateral that they know. Then they pass their notebook to the next student in their group and they need to come up with a different quadrilateral in the next box, then they pass again, and so on. When it dawns on them that they need to come up with 8 unique quadrilaterals the look of dread sets in, they can only think of a square, or question if a diamond is an acceptable shape. Typically the last 3 turns are torture for them and I get a good little laugh. We then share out and they realize they knew a lot more than they thought and typically we get all 8 (the kite being the real struggle, because ‘how is that a shape when diamond isn’t!?’) I share this story because this week, while working on my Introduction to Trigonometry unit, I was challenged to come up with new pedagogies to bring to this unit by doing a quickfire challenge in my CEP 805 course. I had to set a 15 minute timer, add a pedagogy with a quick description, and then add another, and another until the timer ran out. I felt the torture, much as I’m sure my students do, as the minutes pressed on and I had used all of my go to strategies and was now diving into the uncomfortable unknown. However, I then was able to give and receive feedback from my classmates about my ideas and my confidence grew. I was reminded that trying something new in class, while scary, is usually rewarding. Even if it fails there is a lesson there for your students to see - even as teachers we are not perfect, but we are still trying. Two new strategies I intend to implement in my trigonometry unit that are new to me, in this context, are a Gallery Walk and 3-Act-Math. In my gallery walk I intend to have students visit 12 different stations with 3 of each having a different piece of a right triangle being solved for. Each different missing piece will be color coded and there will be matching color post-it notes at each station. Students will copy the picture and steps for solving onto the post-it, hang on to it and at the end look for the pattern in how each problem is being solved. Hopefully they will see that whenever solving for the adjacent side when given the hypotenuse, for example, you use cosine and follow the same steps. The downside being, they are not actually solving. I have done a 3-Act-Math with my students before in Algebra, so I am excited to bring this to my geometry students as it always goes over really well. Dan Meyer, who pioneered the idea of 3-Act-Math describes how this works in the video below. As students work together, they come to a consensus of ‘how it will end’ and you share the final act that shows them ‘the solution’ or the ending of the video. Students are so invested in figuring it out and knowing how it will end that they are eager to get more information to work through and figure it out. However some students can get frustrated with 'not knowing' or the unstructured style of the lesson. Overall, I’m glad this week reminded me that while challenging my students is good, challenging myself to try something new is also good- and can help my students in the long run as well. Resources:
Tedx Talks. (2010, April 13). Dan Meyer at TEDxNYED [Video]. YouTube. https://youtu.be/BlvKWEvKSi8 I think the moment I knew I was truly obsessed with mathematics was during my proofs unit during my Integrated Math 4 class. Given a picture and only a few pieces of evidence, figure out what happened. Looking back this makes so much sense to me because of my love of puzzles, I love deduction style board games, and I love a good mystery that I can try to solve. On the flip side of that I remember the unit I was introduced to sine, cosine, and tangent and felt more lost than I had ever felt in math class. This gave me the impression that I would ‘not be able to teach geometry’. So, of course geometry was the class I was placed in for my student teaching. And after I was hired at my current district, I was made lead teacher of the geometry professional learning community (PLC) because no one else in my department liked teaching the class either. After teaching geometry every year of my career thus far, I have grown to love the class so much. There truly is so much room to play with mathematics in that course and that had never really clicked with me until reading up on a few articles this week about incorporating play into teaching and learning geometric concepts. Play in mathematics is so important and students don’t always appreciate how beautiful and playful it can be (Vasilevska 2021). Having my students fold origami cubes on the first day of class to talk about planes, symmetry, shapes, rotations, and so much more lets me gauge how much they already know about these topics and see their skills in patience and perseverance. Folding the pieces and fitting them together is no simple task - if you’d like to try you need 6 pieces of square paper and you can follow along with my instructions below. Later in the year during our unit on transformations, we create an animation flip book and the amount of creativity that my students come up with each year astounds me. Some students will just do a basic 20 page note card flip book, while others take to programming on a computer, stop-motion animation, or videos of their object sliding, rotating and reflecting within the world they have created for them. I feel that this is one of my strengths in regards to six types of MKT, content and teaching (Hill & Ball, 2009) where the material presented and the level of engagement my students felt to the subject area really aligned. However, while my content and teaching shines in our transformation unit it truly needs work in our surface area and volume unit. Making the connection from 2 dimensions to 3 is an important Common Core State Standard that I need to develop with my students at a deeper level. We do these at the end of the school year so it always feels rushed and there is just a formula to fill in if need be. And even after all these years the dreaded trigonometry unit in some ways is still my weakness, another thing to work on to better the specialized content knowledge (Hill & Ball, 2009). While I have found ways to play with ratios and similarity to make sine, cosine, and tangent make more sense to me, bridging the gap for my students who are not always as obsessed with mathematical concepts as I am is where I am lacking. A final thought on playfulness in my geometry classroom is a board game I came across a few years ago called Mental Blocks. It is a cooperative game that has your team creating a 3-dimensional scene where each member only has some of the information about the scene - be it a side view without color, or an overhead view with color, etc. Not only do I love the cooperative aspect to foster working together in my classroom but the 2-dimensional to 3-dimensional views tie into our geometry standards. And I feel like it could also be argued that having some of the information to create the whole is a bit like how we piece together a proof. I was lucky enough to know the publisher so they gifted me 8 copies of the game to use in my classroom but because of the pandemic I haven’t been able to integrate it yet, but I am so excited to try! Resources:
Vasilevska, V. (2021). From playful math explorations to beautiful origami creations. Utah Mathematics Teacher, 14, 8-19. Misura, M. (2020, September 9). Folding/Putting Cube together! [Video]. https://www.youtube.com/watch?v=TFrkiHFJndk Hill, H., & Ball, D.L. (2009). The curious - and crucial - case of Mathematical Knowledge for Teaching. Phi Delta Kappan, 91(2), 68-71. Misura, M. (2019, August 1). Mental Blocks Demo [Image]. There is a moment that sticks out in my career that sparked my love of Number Talks. I was in maybe my fourth year of teaching and a student answered a difficult multiplication problem really quickly and I was amazed. I asked, ‘how did you get your answer so quickly?’ and as this student described how he got there, he truly opened my eyes to a new way of thinking about how to get to our answer. I grew up and took math courses before the Common Core Curriculum was widely put into place, however I also did not take the traditional math pathway of - Algebra 1, Geometry, Algebra 2, etc. My school taught Integrated Math where a lot of those concepts are blended as well as presented through a real life task and then broken down into smaller skills needed to complete the problem. While I feel that this helps me think about math in more creative ways I still had missed out on some really interesting approaches to numeracy skills. The Common Core Curriculum has a list of Mathematical Practices that hope to promote creative problem solving, make sense of problems and persevere in solving them, define and structure skills that students need to become mathematically proficient that push students to work hard at math. While parents sometimes complain that there are too many steps involved in some of these common core processes, the long-term benefits of showing students subtraction with rounding or multiplication with addition cannot be overstated. One could also argue that taking five or so minutes in my high school math classroom to talk about a simple subtraction problem is a waste of time with all the curriculum I have to teach, but I would argue that these are the skills I want my students to leave high school with perhaps more than memorizing the quadratic formula (however cool and handy that formula is). This fast multiplying student of mine had really changed my thinking about how to come to answers quickly and my love for talking about how you multiplied or how you subtracted became a staple in my classroom. Another really important concept in math that is both part of Common Core’s mathematical practices and National Council of Mathematics Teacher’s process standards is making mathematical connections. For a long time in my career I thought students would just make them. Seeing how the clues to graphing a quadratic are just staring at you in the equation, or finding patterns when looking at slope in a table vs. a graph vs. an equation, was so obvious to me but let me tell you, students don’t just see those things. A small thing I began doing is giving my students ‘helpful hints’ to guide them in the right direction. A major thing I did was rearrange the textbook provided curriculum to follow what I felt was a more ‘linear path’ that connected new big ideas back to smaller ideas we had previously discussed, and I would spell out that connection. Another thing that I feel like has really helped my students is to make them practice being ‘pattern seekers’. This way of thinking came from the amazing Jo Boaler and her Youcubed website (see video below) that has amazing videos to share with your students to give them pep talks concerning how mistakes are good, math is all about patterns, and how making connections is so powerful for brain growth! Rearranging curriculum was not easy, and again taking time away from that curriculum to show videos is hard, but doing this set up at the beginning of the year sets my students up for success for the rest of the year. They look for patterns all the time, they take more chances in class and on homework assignments, and because they understand that mistakes help our brain grow they are more likely to succeed overall because they are less anxious in class about getting the right answer quickly and instead think through the process more carefully. Resources:
Common Core State Standards Initiative (CCSSI). (n.d.). Standards for Mathematical Practice. Mathematics Standards | Common Core State Standards Initiative. http://www.corestandards.org/Math/Practice/ National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. The National Council of Teachers of Mathematics. Youcubed at Stanford. (2021, July 30). Math and Patterns [Video]. Youtube. https://youtu.be/DZ9kXRLvSZU Park, J. (2017). Common Core Infographic [Image]. Bearing News. https://bearingnews.org/293575/features/common-core-math-provides-crucial-problem-solving-skills/# The first few years of every teacher's career is mostly about surviving. Creating lessons, materials, resources, assessments is an overwhelming and daunting task that I remember all too well. By the time I was in my fourth or fifth year of teaching (after only 10 years they all start to blend together but I blame the fact that covid and teaching virtually felt like adding 10 more years onto my career) I realized that I needed to start making more connections between mathematical topics for my students to be able to fall back on or relate new math concepts to. So, I started the creating process all over again. This led me first down the path of ditching calculators in my class almost all together. I came up with the line ‘your Spanish teacher wouldn’t let you use a Spanish to English dictionary on your test, why should I let you use a calculator?’. I don’t know if that totally correlates but it felt right to me. I also wanted a better way to organize and present each mathematical concept to my students so next, I ditched my textbook and began creating Interactive Student Notebooks (ISN) with my students, essentially building our own math textbook. I have stuck to these two important notions each year that I have taught since:
Below is an example of my completed Geometry ISN from two school years ago. I love to have discussions with students about how they subtracted a number quickly or multiplied some really big numbers together. This allows students to gain a deeper knowledge of if their answer makes sense. I love giving students or discussing with students multiple ways to represent their thinking about how to solve a problem. Both of these are crucially important to ways I can bring a MKT, Mathematical Knowledge for Teaching into my classroom (Hill & Ball, 2009). By having our number talks in class to confirm that their answer makes sense we are tapping into our common content knowledge - making sense of answers in all classes is vitally important. We are also using our specialized mathematical knowledge by representing our answers or work in different ways. Skemp (1978) explained how important it is to push students to have a deep understanding of relationships between numbers, which helps me feel validated in my choices to push students to work harder to think in different ways, not use a calculator and sometimes dwell on a seemingly simple math problem for a while. He argues that using tricks and rules to help students get through math are detrimental to their true understanding of the beauty and interactivity of mathematics. However I am absolutely not perfect in this and I love a good math trick whenever I see it and it is difficult to avoid using them when there is so much content to cover in each of the courses I teach. Two big weaknesses that I have tried to tackle over the past few years are teaching logarithms and permutations and combinations. While I definitely feel I have developed in myself a deeper understanding of logarithms and can pass that onto my students I still struggle with how to apply logarithms to something that they can ground themselves in - some sort of real life situation that can make logarithms feel more real. Next I have to tackle my lack of confidence with counting really large numbers and gain a deeper understanding of overcounting and explaining differences in permutations and combinations. Resources:
Misura, M. (2019 August). Interactive Notebooks. [Image]. Hill, H., & Ball, D. L. (2009). [Image]. The curious - and crucial - case of Mathematical Knowledge for Teaching. Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher, 26(3), 9-15. I am very passionate about mathematics education and it concerns me that students struggle so much with the concepts presented. Students often struggle with feeling anxiety in math, or feeling disconnected from it. I feel like more could and should be done about this problem in education. I decided to tackle this wicked problem by doing a bunch of research on why the problem exists, sending out a survey to my peers, colleagues, and students, doing even more research on ways to potentially solve these issues, and then I compiled all of my data in the presentation below. While I didn’t have as many respondents to my survey as I would have liked, I did learn a lot through this process. Not only did I learn how difficult it is to write a survey and consider all possible answers you might like to see, and the high degree at which students are still struggling to feel connected to mathematics and their instructors, but also that editing and compiling all of this information into a well thought out presentation is a difficult task! Overall, we will always have students that struggle with mathematics, but my biggest hope is that teachers will begin to instill in students a growth mindset, share innovative ideas for lessons with other educators, and begin to move mathematics education in a direction that is more applicable to students and their needs outside of the high school classroom. Resources:
Misura, M. (2021, December 16). Wicked Problems [Video]. The past few months have been overwhelming, exciting, stressful, educational, and so many other adjectives. As a teacher, I had to remember how to be back in front of students five days a week. I had to remember how to be a student again because I started my graduate course work at Michigan State University. I am a food, cat, and board game lover. I got married over the summer, and while we have been together for many years, the whole changing your name process is confusing and time consuming! And most recently I learned that I will be adding mother to the list of things that I am. Another big piece of who I am as a person is a maker and creator. The projects I come up with for my students I try to be creative, and when I started making interactive notebooks with my students my creativity really flourished. Throughout my graduate courses so far, the most fun I have is when I get to create some piece of art - whether it was a remixed video, a sketch note video, an infographic, or discovering a new technology, the 3D printing pen, to share with my students - I get so inspired to create something unique. It doesn’t always come together exactly to plan, but most innovators need MANY attempts before they get it right. Take a look at my final creation for one of my classes below. I have been capturing 1 image each day for the past 3 years using the app - 1 second everyday. It is something I look forward to each January 1st to see a summary of the year I just had, along with all the years past that I have done this. It brings me so much joy, I would recommend it to anyone. Resources:
Misura, M. (2021, December 13). 74 seconds of my year [Video]. Based on experience design, the user should be able to flow, participate, and feel some sort of emotion based on the experience you are participating in (Chang School 2010). The experience of being in my classroom I would love to say has a flow - to how the class is run, but also how things are set up, students feel that they are participants in the learning and can participate with each other and I hope that all my students feel safe and comfortable when they enter my room. Take a little classroom tour below! I built a 2D and 3D model of my classroom in floorplanner.com so that I could play with the arrangements of my room to see if I could make better use of the space. My room is small and FULL. Most years I have at least one class that has 33 students, so I have to have the extra group of two student desks in the top right corner just in case. And my 15 - 18 year old students often complain about how cramped it is in my room. I can make it as cozy as I want by adding a carpet, lighting, covering up an unused chalkboard and having a space for all of our tools (and sometimes I get compliments from my students on this) but it isn’t always an inspiring or user-friendly space. I have my students in groups permanently because we collaborate on activities so frequently it would be silly to ask students to move their desks together every other day. Some days our activities are hands-on, however some days we need to access desmos.com (an online graphing calculator) to help us find patterns quickly, while taking notes at the same time and their desks are small and can’t always accommodate all of those tools at once. Having this type of collaboration is key to deep understanding and builds on 21st century skills that students need to develop. In the middle of each group I have a caddy holding supplies they may need (ruler, highlighters, scissors, glue, etc) for creating our interactive student notebooks and other activities, but with those plus the closeness of the desks caddies get knocked over often because of long legs. I don’t often sit at my desk- I try to move around the room and assist students or talk to students from different points in the room as often as possible, so in some ways I wish I could just have it in a separate room. The chalkboard on the left wall is unusable as the windows are directly across from it and the sun shines in on it and make it impossible to read, which tends to affect the whiteboards at the front of the room as well so mostly the shades have to stay closed. After taking all of these problems into consideration I started redesigning my room with no budget, only hopes in mind. I would love to have tables with comfortable rolling chairs for each student and an all-in-one computer or tablet for each group for easy, quick access to desmos (or any other web-based tool) whenever we need it. In addition I would like to have the option for students to sit at high-top tables as well, the 6 tables around the outside would be high tops, again with adjustable rolling chairs. Personally, as someone who is tall, the extra space this provides for my legs is so appreciated. I would add white boards all around the room, updated projectors also in multiple locations, and better window coverings so that the sun does not impede students' views of work on the boards or projectors and can still be enjoyed. Also adding in movable smaller whiteboards for students or myself to bring to a group and have them work out problems together or with me. I would love to add all these features to my classroom as we have seen in studies that taking into consideration the space we are learning in as a tool to enhance learning can benefit students greatly, if only we all had the means to do so. Resources:
Chang School. (2010, February 9). Tedde van Gelderen on experience design. [Video]. Youtube. https://www.youtube.com/watch?v=BB4VFKn7MA4&feature=emb_logo Misura, M. (2019) Classroom Tour [Video]. Misura, M. (2021, December 7). Classroom views [Images]. Misura, M. (2021, December 7). Classroom Floorplans [Images]. Misura, M. (2021, December 7). Redesign Classroom [Images]. One of my favorite topics to teach is surface area and volume of 3 dimensional shapes because students can see how math comes to life. What better way to engage my students even more than by adding a MYNT3D printing pen to the mix so that they can truly become creators themselves! A project that I have done for years in my geometry class during this topic is to have my students create a ‘prism person’ where students create nets (2-dimensional representations of 3-dimensional prisms), cut them out, tape them together, and create some really interesting characters. This seemed like the perfect lesson to use my printing pen for as students often struggle with cutting, taping, making their prism person stay together, and creating a net that will completely come together. My first draft of this lesson went through a lot of edits and received a lot of feedback as any good lesson should! See my feedback below. I also was tasked with giving my classmates in CEP 811 feedback on their lessons through two different lenses - intersectionality and Universal Design for Learning (UDL). Reading through my feedback and giving feedback through those lenses gave me a lot to think about as I started to revise my lesson plan. Considering that students may struggle with fine motor skills would make it a challenge to complete the task and the ever looming difficulty of convincing students who do not love math that completing this task has value to them. It was also interesting to read one of my classmates' lessons that was for an English class that integrated math and CAD (computer-aided design) into his lesson and gave me inspiration to add a writing component to my lesson. After looking through my combined feedback the biggest thing I knew I needed to create was a rubric. Having clear guidelines for my students and myself as to what needs to be accomplished was always lacking in past years of completing this assignment. In addition to that, extending their learning outside of just surface area, volume, and characteristics of prisms was an excellent suggestion from one of my classmates. I incorporated both of these aspects into my final lesson plan. Overall the basic outline and flow of completing the task remained the same. On top of considering my professor and peers' feedback, we were also asked to consider research articles that support our task, or could enrich our task. In an article from NCTM, or National Council of Teachers of Mathematics, by Melinda Eichhorn et.al that focuses on using UDL to build the optimal learning environment for learning she mentions that “UDL,..., provide(s) students with options to access challenging tasks within the curriculum” (Eichhorn 2019 p.263). This convinced me to keep part of the old assignment (paper prism people) as another option or another viewpoint of creating a prism. I also created a pop-up-like book for students to pull on strings to make the nets come together. Another article, Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D print, focused on specifically using a 3D printing pen as opposed to using an applet to simply view 3-dimensional objects to learn about their different characteristics. The findings of this study were very interesting. Overall the study concluded that while students using the dynamic geometry tools alone performed better on their posttest, the students using the 3D printing pen had more significant retention of the material as another posttest was given much later (Ng et. al. 2020). Using this information I decided to also add in a desmos activity so that students could visualize the objects on a computer to try to give even more options while including a digital aspect, for students to better visualize and understand the task. Overall, after considering multiple viewpoints, getting tons of feedback, and supporting any changes with research to back it up, I feel that this activity is in such a better place for my students. In an ideal world I would have 32 printing pens, the filament for my students to create to their heart's content, and it would be May so that I could do this activity tomorrow! Resources:
Misura, M. (2018). Prism People [Image]. Misura, M. (2021, November 29). Lesson Plan Feedback [Images]. Misura, M. (2021, December 3). Lesson Plan FInal [Images]. Misura, M. (2020, May). Net Pop Ups [Image]. Eichhorn, M et. al. (2019). Building the Optimal Learning Environment for Mathematics. National Council of Teachers of Mathematics, 112(4) 262-267. https://doi-org.proxy1.cl.msu.edu/10.5951/mathteacher.112.4.0262 Ng, O., Shi, L., & Ting, F. (2020). Exploring differences in primary students’ geometry learning outcomes in two technology-enhanced environments: dynamic geometry and 3D printing. International Journal of STEM Education. https://stemeducationjournal.springeropen.com/articles/10.1186/s40594-020-00244-1 |
AuthorMarissa McGregor, high school math teacher extraordinaire. I love my husband, daughter, and family dearly. Archives
August 2022
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