Portfolio Journal: Expanding Students Conceptions of Mathematics

Here is the last section of the Portfolio journal that my students will be keeping this school year. It is the least-complete of the three sections as it is still an active work in progress. I’m working with Sam Shah on this and I’m SUPER excited about its potential, albeit slightly overwhelmed at the logistics of creating the resource library for students.

I have 12 weeks with my students in which I feel comfortable assessing them. I have an additional opportunity in the form of a “Final Exam” for the course that will be a take home exam students will complete upon their return to their houses after Thanksgiving. I plan to use that final exam for the reflection part of this Expanding Math Journal.

Before I dive into the Expanding Math Journal I need to give you an overview of my expectations for student’s outside of class life: I will be flipping the classroom, students will be watching short (5-10 min) videos on content that we will then practice in the next class block. We have academic classes 4 days a week. In addition to watching videos I expect students to spend the week’s “HW Time” working on their deliverable for the week, aka their portfolio submissions for the week. Therefore I am expecting a total of approximately 2 hours of asynchronous work time; 40 minutes for watching lesson videos, and about an hour and twenty minutes for working on the week’s content. I have 12 weeks, so 6 of those weeks students will submit a Capstone Journal Task, which I have talked about in my previous posts, and the other 6 weeks students will submit a topic for they Expanding Math Journal.

Expanding Math Journal

I haven’t written my prompt to the students yet, but the general idea is:

During the first week of class I has asked you to write a little about your responses to the following questions:

– Who does math? What does a mathematician look like? (encourage them to draw a picture)

– How can math be used for the benefit and detriment of society?

– What is Math? Write your definition of math using your own words.

You entire mathematical history has been spent exploring a rather slim branch of the mathematical family tree. In fact, you’ve probably spent most of your time exploring these 4 bubbles of mathematics:

https://mymodernmet.com/science-infographics-dominic-walliman/

The goal of the Expanding Mathematics Journal is to widen your understanding of what mathematics is, to rethink who does mathematics, and reevaluate your lens on how mathematics is used in society. This semester I will be asking you to complete 6 of these Expanding Mathematics Journal Entries, and your final exam for this course will be a reflection piece on how your Expanding Mathematics Journal and your Capstone Journal has changed or expanded your perception of mathematics and learning.

The Expanding Mathematics Journals will cover three categories, you are to do two entries from each category this semester. The categories are:

1. Who does Math?

2. Intersections of Math and Society

3. Expanding Your Definitions of Math

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And that’s what I have right now. Like I said, it is still very much a work in progress. The idea is students will create a deliverable for each week that shows off their learning. That “deliverable” can look really different from students to student, but I’m envisioning sketch notes, or a summary, possibly a video of them explaining a new math concept they learned. But what I do know is that students will be reading articles, chapters from books, and watching videos about these three topics. Some sample ideas on what they will be exploring:

1. Who Does Math?
   • Annie Perkin’s #NotJustWhiteDudes project
   • Mathematically Gifted and Black
   • Meet a Mathematician
   • MAA Mathematician Blog-Living Proof
2. Intersections of Math and Society:
   • Read some chapters from Weapons of Math Destruction, by Cathy O’Neil to see how algorithms are used. I particularly want them to read the chapters on algorithms and college, getting a job, or credit.
   • Read a chapter from The Art of Logic: How to Make Sense in a World That Doesn’t by Eugenia Cheng. In particular the chapters on the directionality of logic, opposites and falsehoods, and blame and responsibility.
   • Moon Duchin’s Podcast on Gerrymandering or Vi Hart’s Gerrymandering interactive blog the Parable of the Polygon.
   • Podcast: Wrongfully Accused by an Algorithm
   • And a collection of articles about mis-representing mathematics
3. Expanding our Definition of Mathematics
   • Annie Perkins (She’s awesome) $MathArtChallenge on her blog
   • Pretty much any Vi Hart or Numberphile video
   • Islamic Geometry Design videos
   • Mathematical Games like the ones Ben Orlin posts over on his blog, the ones in Francis Su’s book Mathematics for Human Flourishing

And this isn’t an exhaustive list. Sam and I are still collecting resources and trying to figure out the best way to get those to our students. He’s got a slightly different plan for this than I’ve outlined, but it has been really fun having a thinking partner for this project. I’m really excited.

Student Self-Evaluations: The Game Plan

For those of you just now joining the conversation: I’m having students build a portfolio this year. It will make up 70% of their grade. I talked about the content-heavy portion of the portfolio here. Up next in the portfolio journey is the student self-evaluation section, which is what I want to talk about today.

The basis of this section of the portfolio comes from Cindy Reagan‘s blog here and listening to her Global Math Department webinar on reflection in math class. I highly recommend the talk. It is an amazing hour and overmuch worth your time. Listening to her GMD talk was the push I needed to get moving on this idea for a portfolio.

Here is the prompt I’ve given students in regards to the self evaluation portion of their portfolio:

Throughout the school year you will be asked to reflect on your learning in this section of your journal. Reflection is an important part of the learning process and I wanted to make sure that we structure time this year to check in on your learning and how you are feeling about the class. There will be two kinds of prompts for this reflection journal: 

Weekly Reflection Prompt

We will complete on Tuesdays after you take your Standards Based Grading Assessment.

Think back about all of the math that you have experienced this week. 

1. What is one problem or moment from our in-class discussions or practice that you are proud of? Tell me a little bit about why. 

2. What is one problem or moment from our in-class discussions of practice that you are still feeling unsure about? Tell me a little bit more about the problem you are having. Feel free to upload a photo of the work you’ve done so far. 

3. Optional: How are you feeling this week? Is there anything that you’d like to tell me that would help me better support you right now? Are there any comments or suggestions you’d like to give me about class? Remember, I’m new at this online thing too, so constructive feedback is helpful and welcome!

Monthly Self-Evaluation Prompt

We will complete on the last Tuesday of each month (Sept. 29, Oct. 27, Nov 17) in place of your weekly submission. 

I’d like for you to take a few moments and reflect on your learning from the past month, then take a look at this rubric and give yourself a grade on the components listed. I’ll remind you that this is self-assessment, I am not grading it, but I think it is a good conversation starter for us. The grades/percentages listed are just to help you navigate the rubric. 

Cohort Group Contributions
A (100-90%)	B (89-80%)	C (79-70%)	D (69-60%)
You question your own work and the work of others. You practice active listening and are respectful of the ideas, comments and solutions of others.	Your questions are usually to clarify your own understanding of a concept.  When confused, you might lose the ability to listen to others.	More often than not you are not listening and/or are not engaging in discussion with your classmates or teacher. You largely rely on other to make connections for you.	You rarely engage in class discussion in a productive way.

Learning Participation
A (100-90%)	B (89-80%)	C (79-70%)	D (69-60%)
You consistently watch the HW Video lessons prior to class and come to class prepared with questions or thoughts. Your portfolio entries are turned in on time and are complete.	In general, you watch the HW Video lessons prior to class. You sometimes come to class prepared with questions or thoughts. Most of your portfolio entries are turned in on time and they are complete.	You often are not watching the HW video lessons prior to class and/or frequently come to class not prepared with questions or thoughts. Your portfolio submissions are often turned in late and/or are incomplete.	You are not watching the HW video lesson prior to class and/or you do not come to class prepared with questions or thoughts. You are not completing portfolio submissions.

Capstone Journaling
A (100-90%)	B (89-80%)	C (79-70%)	D (69-60%)
Your capstone journal entries are well organized and contain accurate math. You show your revisions/expansions during the problem-solving process and are engaging in reflection of your learning.	Your capstone journal entries give a clear approach for solving the problem but sometimes you forget to write the entire mathematical process or have difficulty communicating your math.  Your revisions/expansions while problem-solving are somewhat incomplete and/or you are not consistently engaging in reflection of your learning.	Your capstone journal entries are poorly organized and/or offer incomplete or inaccurate mathematical processes. More often than not you have difficulty communicating your math.  Your revisions/expansions while problem-solving are largely incomplete and you are not thoughtfully engaging in reflection of your learning.	Your capstone journal entries are incomplete and do not communicate your mathematical thinking.   You do not offer any revisions/expansions on your problem-solving and do not provide any reflection on your learning.

Advocacy
A (100-90%)	B (89-80%)	C (79-70%)	D (69-60%)
You are an active advocate for your learning and often advocate on behalf of your peers.	You are an advocate for your own personal learning. You have difficulty helping others with their learning but you make an effort to aid your peers in their understanding.	You find yourself resistant to advocating for your own personal learning and tend to find excuses for not reaching out for help. You do not actively assist your peers in their understanding.	You do not engage in any advocacy for your learning or for the learning of your peers.

Once you have given yourself a score on the above rubric, I’d like to hear your thoughts on the following prompts:

1. The area I’ve experiences the most growth is…

2. The area that I feel I am the weakest is…because…

3. My plan for improving in my area of weakness is…

4. What I want Mrs. White to know right now…

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Right now I plan to grade these on completion, but I may change my mind on that. I really just want these to work as check ins with students and as launch points for remediation conversations. I don’t want a repeat of Spring 2020 when I had kids spiraling and didn’t have enough checkpoints with them to aid in a timely fashion.

Capstone Journaling as an Assessment Tool

So in my last post I gave you some of the background into my first attempt at journaling in a math class. I’ve been chewing on the idea all summer: how to scale this up from a task we did just one time in pandemic learning, to a routine for engaging in math that I feel comfortable using as an assessment of student learning.

In an effort to wrap my head around this idea I spent the summer reading Rough Draft Math by Amanda Jansen and Up for Debate by Chris Luzniak. And, in full disclosure, at around the Late June stage of the summer I had a meltdown. I loved every routine in each of these books, I wanted to badly to get back to my pre-pandemic classroom and have students engage in mathematics together like normal and I hate Covid and I hate that the 2020-2021 school year is different and…

I cried. A lot. And I was in an anxiety spiral for most of July, because, well that’s what teacher planning for the month of July looked like. I don’t know a single educator who made it through July without their own breakdown. I think that’s because we never stopped. We’ve been going full tilt since March trying to wrap our heads around how to do this the best way possible for our students. Then, as it always does, a conversation from Twitter got me thinking again. I CAN use all of the rough draft thinking routines and the debate math structures…I just need to get students writing.

For the 2020-2021 school year group work is out the window for me. That’s not an option, in the traditional sense of 4 people sitting around a desk working on the same problem at the same time and sharing manipulatives kinda way. At least not for me. I’ll be teaching online but most of my students will be on campus (in a hybrid model with cohorts to minimize students on the hall). I’ve tried problem solving in groups on Zoom. I was in a PD just last week where we were sent into breakout rooms to work on a problem with 3 strangers from the internet. 3 strangers with more experience in the math we were studying than I had. I hated it. Every second was like pulling out my fingernails. People talked out loud about the problem too soon. To use a Fawn Nguyen reference, they “spoiled” the problem for me. I hadn’t even begun to wrap my head around the problem before someone told me the answer. It sucked.

And that reminded me of a student’s feedback from the journal prompt I gave in April. She’s a quiet kid, doesn’t really like group work because of all the reasons I just said about the Zoom call. Her processing time is longer than that of her peers. She likes to chew on a problem by herself before jumping in with her peers. She said, “[The journal structure] was the first time where I felt like I got to math on my terms and not yours.”

Aside from being the slap in the face I needed. (I love the brutal honesty kids give you once you show them you care about their feedback and will use it to make changes in your instructional practices.) It caused a bunch of things to click together for me. And I had a plan.

The Journal Plan:

The main ideal I liked about Rough Draft Math was to interrupt student thinking during a problem and to have them share out their rough draft ideas. Their incomplete thoughts on a task. The main take away from Up for Debate was to get students to write compelling arguments that have both a claim and a warrant that will convince a peer of their thinking. 2 year ago I read Necessary Conditions by Geoff Krall and it changed my teaching life. I adored every page of the book and last year I started having students create a portfolio of their math learning by having students complete Anchor Problems. He recently did a blog post that summarizes the idea quite nicely here. [Sorry if this paragraph feels like an ad for Stenhouse, but what can I say, they publish a good math book.]

So it’s time for a mash up. Here’s what I’m giving students to explain our Anchor-Problem-Rough-Draft-Debate-Journal:

Capstone Problems 2020-2021 School Year

Throughout the school year you will have several opportunities to demonstrate your understanding of the skills you have acquired while learning geometry. We will call these problems Capstone Tasks and you can think of them as journal entries into your mathematical diary. I call them a diary, because I would like for your Capstone submissions to have a fair amount of reflection on your thinking in them. Here is a general sequence of events that we will use for our Capstones:

Step 1: Read the Question & Form a Hypothesis

Beginning of a new unit: we will read over the capstone options (there will be some choice on your end as to which of the capstones you complete in some circumstances). You will journal in your document and record what information you believe is important and you will make a hypothesis. 

Step 2: Marinade on Your Thinking

We will put the capstone aside and start the unit. Occasionally I may ask you to look at your hypothesis and reassess. You may share your hypothesis with some peers and compare and contrast ideas. The goal of these tasks is to make your thinking visible. So, if you no longer believe your hypothesis will be true, that’s fine, don’t erase old thinking! Rather, say why your thinking has changed and what motivated that change in your thinking. 

Step 3: Test Your Hypothesis

At the end of a unit you will be asked to test your hypothesis. Show your mathematical thinking and support that thinking with diagrams and/or other visual aids when necessary. 

Step 4: Revise or Expand Your Solution Path

If you find an issue with your solution path while testing your hypothesis, I want to hear about it. What was your mistake and how/what did you learn from it? What do you think about the problem now that you have a new idea for how to solve it? What are your next steps? What alternative path will you take to find a solution? 

The important part here, and possibly the new part for your math education, is to not erase any old thinking. You can strike through it, and explain why you’ve changed your mind, but let us not pretend it never happened. Learning occurs in that process of changing your mind, I want to celebrate that!

If you didn’t run into any snags in your solution path, you’re still not done here. There is always place for expanding on ideas or clarifying your thought process. The goal is to ensure the reader of your work has full understanding of your thought process, so make sure that you didn’t leave anything out. 

Step 5: Reflections

Okay, so you think you’ve got a solution for the problem? How confident are you in your solution? Explain. Discuss how the solution or problem-solving path connects to other topics.

And in this moment, you may find yourself thinking, “Wait Mrs. White, isn’t that basically the Scientific Method?” Why yes. Yes, it is. I adore this framework because there is a built-in method for changing your mind or revising and expanding your thinking based on new information received in the research process. The idea of revising your thinking is an act that I think needs to be celebrated a little bit more in life. 

These assignments will be graded on a rubric that scores the rigor, or the “convincing-ness,” of your mathematical argument, your reflection on your learning during the task, alongside your demonstration of the skills learned throughout the unit. You will have two opportunities to submit each of these capstone tasks, and the second submission will come with an extra reflection prompt to aid in your revisions. But, as you’ve guessed, I don’t want any old work erased, just a focus on a change in your thinking and your new train of thought for solving the problem. 

And if you’re wondering how I plan to assess the students on this, fear not, I have a rubric for that. It is largely inspired by the New Tech Network’s Problem Solving Rubric for grade 12 here.

Geometry Capstone Rubric

(Adapted from New Tech Network Knowledge and Thinking Rubric)

	Emerging (0)	Developing (1)	Proficient (2)
Problem SolvingWhat is the evidence that the student understands the problem and the mathematical strategies that can be used to arrive at a solution?	Does not provide a model Ignores given constraints Uses few, if any, problem-solving strategies and tools	Create a limited model to simplify a complicated situation Attends to some of the given constraints Uses inappropriate or inefficient problem-solving strategies and tools	Creates a model to simplify a complicated situation Analyzes all give constraints, goals, and definitions Uses appropriate problem-solving strategies and tools
Reasoning and ProofWhat is the evidence that the student can apply mathematical reasoning/procedures in an accurate and complete manner?	Provides partially correct or incorrect solutions without justifications Results are not interpreted in terms of context	Provides partially correct solutions with justification or correct solutions without logic or justification Results are interpreted partially or incorrectly in terms of context	Constructs logical, correct, & complete solutions with justifications Results are interpreted correctly in terms of context, including addressing reasonableness of the final answer
Communication and RepresentationWhat is the evidence that the student can communicate mathematical ideas to others?	Does not use representations (diagrams, tables, graphs, formulas) or uses few representations in a way that confuses the audience Uses incorrect definitions or mathematical notation (units of measure, labeled axes or diagrams, equation formats, etc.)	Uses representations (diagrams, tables, graphs, formulas) that provide help the audience follow the chain of reasoning in a limited way Uses imprecise definitions or incomplete mathematical notation (units of measure, labeled axes or diagrams, equation formats, etc.)	Uses multiple representations (diagrams, tables, graphs, formulas) to help the audience follow the chain of reasoning with accuracy Uses precise definitions and accurate mathematical notation (units of measure, labeled axes or diagrams, equation formats, etc.)
MetacognitionWhat is the evidence that the student has reflected on their thinking process in problem solving and that they have	Does not challenge or expand upon their previous thinking when given new contexts  Does not demonstrates an evaluation of their revision/expansion process during the problem-solving task Makes little or no connections between expansions/revisions in their work and new knowledge gained from the course	Challenges or expands upon their previous thinking when given new contexts but does not consistently articulate these changes in thinking clearly or with confidence Demonstrates an incomplete evaluation of their revision/expansion process during the problem-solving task Makes loose connections between expansions/revisions in their work and new knowledge gained from the course	Challenges or expands upon their previous thinking when given new contexts & articulates these changes in thinking clearly & confidently Demonstrates a thoughtful evaluation of their revision/expansion process during the problem-solving task Articulates connections between expansions/revisions in their work and new knowledge gained from the course

I have collected a bunch of the Anchor Problems for geometry. Tasks that are defined by having multiple entry points and ideally multiple paths to a solution and/or multiple solutions. I’m leaning heavily on MenuMath type problems or Would You Rather structures to add in the sense of Debate. I’ll write more about those soon.

Reflecting on Spring 2020 and Thinking Toward 2020-2021

Hello friends, long time no blog. Every August Shelli posts #MTBOSBlaugust prompts and every year without fail it gets me over here to this blog to write some things down. So hello 2020-2021 school year, how the hell did you get here so fast?

Like most of you, I spent all of the Remote Pandemic Learning portion of my Spring 2020 semester in crisis management mode. I wasn’t sure how to do anything and felt unsure of every move I made the entire time. Well I was unsure of every move but one: I asked students to journal as they worked a Menu Math Task (the Building Quads one by Amie). My students gave me the most thoughtful reflections on their working I’d seen all year. I cried literal tears of joy grading these papers. They were beautiful, and the motivation to how I plan to assess most of their learning this school year. But before I get there, here’s an overview.

The structure:

I gave my students the following prompt:

Hi math family, this task is going to have a slightly different structure than the capstones we’ve submitted so far this year. I want this one to read like a journal entry with stream of conscious writing for how you approach this problem.

Step 1: State your hypothesis, what do you think the solution to the problem will look like? Why? (don’t go too much into the math here, but stake your claim to what you think the answer will be

Step 2: Test that hypothesis. If it doesn’t pan out, don’t erase it, but talk about why you’ve had to change your mind.

Step 3: Revise your hypothesis and repeat step 2

Step 4: Proudly state your conclusion and let me know how confident you are in the results.

Here is an example from one student, who did, in fact, go on to write more on the next page

Then another from a student who took the journal entry structure to heart and I was here for it.

I adored how thoughtful even my most reluctant remote learning student was in their completion of this problem. So I reached out to a few students and asked them a bit about the task structure and I heard back an overwhelming “It felt so low stake because you literally told us it was okay to scratch out bad work and just keep going.” “It didn’t need to be perfect, you actually wanted our messy thinking and that felt do-able.”

My favorite submission remarked on how their solution would have been more elegant without the need for a reflex angle. ELEGANT! Every geometry teacher in the world lives to hear a student strive for elegance in their thinking.

So I have found a structure that is inviting for students: Journaling. And I’m not sure about your students, but mine are REALLY into bullet journaling, so I got some freaking beautiful entries so in addition to journaling giving students a low-stakes entry to mathematics they are a pleasure to read. Win-win.

This is going to be a series of blog posts because the portfolio that I want students to create this year has several components:

1. Capstone Journaling as an Assessment Tool
2. Student Self-Evaluations
3. Math in the Wild: Expanding Students Conceptions of Mathematics

So thanks for reading, and stay tuned for more tomorrow.

Reflecting from a Distance

I’m not sure about y’all, but the transition from teaching in my classroom to teaching from my home office while wrangling a 4 year old was…well, let’s just call it “interesting” and leave it at that.

I survived the transition to remote learning with the help of the amazing online group of educators I’ve found and friended on Twitter. We shared our victories and our defeats, what was working and what was definitely not working, our hopes and our dreams, and our worries for what comes next. The community shared Desmos collections of eLearning activities, technology tools to aid in online collaboration, suggestions for physical math packet making/content, productivity hacks to keep track of all of the things, and methods for checking in on our students and keeping communication open with families of our students. My twitter feed became an overwhelming collection of things that looked amazing, but I no longer had the bandwidth to follow along as my school year came to a close. I suspect I was not alone in wanting to try to collect all of these resources while teaching, and that’s how this idea got started.

The Goal:

The goal of Reflecting from a Distance is to continue the sharing that started on twitter during this transition to remote learning as we look towards starting a new semester with a lot of uncertainty with regard to what the semester will look like. Will we be face-to-face? Will we be remote? Will there be a hybrid model of face-to-face and online? Will we start face-to-face and then have to abruptly re-transition to remote? Honestly, we don’t know; what I do know is that planning for what’s next will ease a lot of my anxiety, and from what I read on twitter, I’m not alone.

The inspiration for this initiative comes from a question asked by @druinok on twitter:

The tweet collected a lot of traffic and had some really good ideas from those of us whose students have access to the internet and a device. The thread had more teachers with synchronous learning environments, and the responses skewed towards high school teaching, with a few middle school teachers. To quote @mrsstipemath:

The tweet reads: “Middle school distance learning is not equal to high school distance learning is not equal to college distance learning” [person shrugging emoji]

So, in the theme of learning from this online community and implementing that learning through action: I asked, “Whose experiences are missing?” I noticed a lot of white voices and a lack of representation from teachers of students without internet or devices, in asynchronous environments, and the responses provide little to how experiences changed across elementary school and higher education experiences.

This blog doesn’t serve as a critique of the thread as much as the motivation for why we need to move the conversations from twitter, and its inherent silos, to a platform that is actively working to amplify the voices of under-represented teacher groups online and has experience sharing the amazing work that educators from around the world are doing daily in their classrooms: The Global Math Department.

While we are on the thread of thinking towards our next steps and navigating the tension between teaching in a pandemic while living in a pandemic I want to make sure we focus our energies on how we can humanize our students’ experience in our remote classroom. Back in November 2019, in what feels like a different lifetime, Hema Khodai (@HKhodai) participated in Making Math Moments Matter Virtual Summit (the summit was free at the time, but now requires payment to participate) and gave a session titled Who is a Mathematician.

The talk was an exemplar of how online learning could be structured to engage students, but more importantly Hema cites Dr. Rochelle Gutierrez (@RG1gal) in the need for math teachers to have multiple types of knowledge: content, pedagogical, political, and of diverse students. Math is not neutral and, as math teachers, we are not apolitical. Then, Hema shared a quote that I come back to over and over again in my daily planning, which has been at the forefront of my mind in these remote learning days:

“How can a fractured educator teach the whole student?”

               -Hema Khodai, November 2019

Hema and Dr. Gutiérrez were referencing the internal work educators need to engage in to ensure that we are routinely confronting our own personal biases while actively questioning our practice of teaching and the impact that those actions have on our students. As educators, we need to view our teaching through a critical lens to ensure that we are not inflicting harm on our students. Use of instructional methods or practices that disregard the intersectionality of the identities of our students, that fail to see our students as a whole, actively cause harm. It is our work of learning (and unlearning) to continue to shape our practice in ways that allow us to see all of our students as whole.  This same reflection is needed as we critique our remote teaching practices to ensure they are addressing our students holistically.

So I challenge you to think of all the things that are draining for you, as the educator, right now in your remote teaching. If we, the adults in the remote classroom, are having a hard time with the over-abundance of Zoom meetings, the bombardment of emails and notifications, the cluttered calendar, and feeling like the foundation of our teaching practice is fractured, how do you think our students are feeling?

Collecting Videos:

We are working with the Global Math Department (GMD) to collect short videos (5-6 minutes) and blog posts of what you learned from our remote learning experiences from January 2020-June 2020 that worked for you and your students so we can be better prepared for what’s next in our teaching. 

Did you, in your experience of remote teaching, find success with:

1. Tech Tools: You can go big picture and show us a learning tool (like EdPuzzle, ClassKick, SeeSaw, or some other platform) or show us how you create content within a tool (like pacing on Canvas or your LMS, creating assessments with Google Forms, or something else).
2. Tasks: Did you redefine what a mathematical task looks like, for learning or assessment, during the remote learning phase of teaching? Is it something you want to share with the world?
3. Productivity Hacks: Remote learning posed a whole new mountain of stuff for teachers and students to balance. Did you find a system for organizing your thoughts, documenting student communication, helping students stay on top of their work, or some other productivity hack?
4. General Big Picture Take Aways: In harking back to Hema’s virtual conference session, what ways have you found to help humanize the remote learning experience for your students? Have you found a system of checking in with students on their emotional health and well being that you will continue to use next semester? 

If you, or someone you know, has done something during this remote learning phase of teaching that you think others may find informative or useful, encourage them to submit their video(s) and tell us a little bit about their remote teaching experience on the google form linked here (and also available at the end of the blog post).

We ask that all video submissions contain closed captioning for those members of our community who would benefit from having a text transcript of the contents of the video. Apple Clips, a free app for recording that works with iOS devices comes recommended from our #DeafEd community. If you record with Screen-Cast-o-Matic and the Camtasia suite of video creating tools there is an automated closed captioning feature in the edit feature (Speech to text) that is very easy to use. Kapwing is another option that is web-based for creating closed captioning in your videos.

We are accepting submissions until June 30th, 2020 at 11:59pm EST. The videos will be tagged with descriptors and then added to the Global Math Department’s Youtube page. 

Thank Yous

Thank y’all for reading this post to learn about how we can continue lifting each other up as we move forward into the unknowns together. If there is one thing I know for sure, it’s that:

• 

From our friends at @BitterSouth https://bsgeneralstore.com/collections/bitter-apparel/products/teachers-t-shirt

 

Google Form for Video File Submissions:

Online Teaching with Desmos: Self Checking Tasks

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UPDATE: July 24th, 2020

Howdy new-to-this blog post friends. I’ve noticed a lot more traffic here so I wanted to clarify a few things about this self-checking template that I made: It was made out of a need to continue the formative assessment structure I already used in class, NOT for summative assessments. My school, when we shifted to remote learning, went asynchronous, and I had students across 21 hours worth of time-zones spread out all over the world. I needed a quick way to get the instant feedback my students were used to from doing card stacks and other self-checking in class practice of content (see my blog post here on my 1/2 and 1/2 structure for a face to face classroom). So I guess that’s my long-winded way of saying, “I threw this together quick with little regard to pedagogy” cause the quick shift to pandemic remote learning was HARD.

I wanted to clarify the above because I think people, myself included in this for what it is worth, have been using these templates in a way that doesn’t really align to the best practices of Desmos usage. I made these templates in a rush. Using the CL knowledge I had to survive pandemic remote learning when I, naively, thought we’d get back to campus in a few weeks. I really did think these templates would get used 3 or 4 times, and then we’d all be back together and mathing in my classroom. I was wrong. We are not over Covid, and we teachers need to find ways to use Desmos remotely AND still uphold using Desmos as more than a worksheet with solutions you know? What I love most about Desmos is it is interactive with my students, I want to think critically on when I want Desmos to be a checker instead of a collaborator with my students learning.

I made these templates before Desmos introduced the chat feature (which is amazing!!). I didn’t know that I’d be able to communicate with my students INSIDE a Desmos AB when I pieced together the CL to make this happen. Desmos evolved, and so will my use of Desmos next school year.

So, if it helps, here are my thoughts on planning for the 2020-2021 school year, which will be a combo of hybrid and online in all likelihood, and in which I will retire the templates from my teaching practices (I’m not deleting this post, or the templates because I believe in modeling growth in learning and changing of ones mind):

It is with that, if I haven’t convinced you that we can do better as math teachers than just my self-checking templates, you can keep on reading friend. I get it. Sometimes you just need kids to know if they did a problem correctly. But know that I’m not going to use these as is next year because I think I can do better by my students and I encourage you to join me in thinking on that. How can we use self-checking code for a better-than-worksheet-checkers?

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Howdy internet friends,

It’s been a while. That’s mostly because I haven’t really been overtly proud of anything new I’m trying this year. I’ll blame it on having spent most of the semester solo-parenting a toddler, but its really just that when life gets hectic this blog is the first thing I let go of.

That being said, right now everything is feeling very uncertain with the Covid-19 pandemic and I find comfort in helping people. So here it goes, I want to offer to the internet world something that’s been helpful for my classroom when I want to leave students with work, that provides feedback, when I am absent.

I do a lot of Card Stacks (see @MathEqualsLove blog post here) in class so students can practice new skills and get immediate feedback on how they are doing. Due to parenting a toddler and needing to be out often I started creating Desmos Activity Builder versions of these card stacks. I thought that perhaps people would like a template they can copy and edit to create their own.

Desmos Activity Builder Self-Checking Template: Card Stack Version

If you are semi-familiar with the computer coding access that you have in Desmos called Computational Layer, then you know the drill. Go ahead and edit away and be sure to adjust the input CL’s correct value.

If you’d like a tutorial, keep on reading:

Step 1:

Log into Teacher Desmos and click on the arrow by your name in the upper right corner.

Step 2:

Check your Desmos Lab Settings. Click on the triangle by your name. Then click Desmos Labs. We need the Desmos CL box to be on (checked)

Step 3:

Okay, now navigate to my activity here. We want to create a copy for you to edit

And you will be redirected to a new window with the editing features of a Desmos Activity Builder.

Step 4:

I made the activity so you only need to adjust two parts on each slide to have the self-checking feature work. The first thing we need to adjust is the CORRECT ANSWER. Click on the gear by the input component.

You will see a new window appear for editing Desmos Computational Layer code that looks like this:

You only need to change the BLUE number. Please change the blue number 1 to what ever you want your answer to be for the question. Once you’ve completed the correctness edit, click Done. 

Step 4.5: UPDATE from 3/18

So as I am making an activity I’m realizing that I want directions in the note component. Here’s how to do that:

Then replace  the text “Enter 1” with what ever you want the directions to be for the students. Leave the code at the bottom alone.

Step 5:

Adding your question. This AB assumes that you will be taking screen shots of questions and posting the image inside of the graph component. So have all screen shots ready to go before you continue.

Click on the Graph Component

And then add the image to the graph. You will need to re-center the image and scale so it can be seen.

Click done once you are happy with the image. Congrats. You’ve edited one slide!

Step 6:

Do all of that again for all of the slides you want to use. If you don’t need 10 questions, delete the slides you won’t use.

IF YOU WANT MORE SLIDES:

Duplicate a slide, then you will need to adjust the LABELS on the components (note how mine said input9, you’d have to make an input11 for slide 11) and then update the numbers in the Cl for the NOTE (click the gear by the note) accordingly.

Have questions? Tweet me. @JennSWhite

1/2 & 1/2 Classroom

So for those of you who know me, you know that I love coffee. Like, LOVE COFFEE. I don’t drink it black, even though I know I should. It needs a dash of sugar and a splash of 1/2 & 1/2 to reach perfection.

Why did I mention this? Well because my brain is dead and the title had 1/2 & 1/2 in it and I needed an intro. Let’s focus on the point: What 1/2 & 1/2 has to do with my classroom.

The other day I got into a convo on twitter here (oh and look at that. It starts with a GIF about coffee. So #onBrand and makes this into look planned) about why I like routines in my classroom. In particular how smaller routines fit into a larger routine that is the 1/2 and 1/2.

The Large Routine- a.k.a. The 1/2 &1/2:

I strive, for each period with my students, to spend 1/2 of the class period practicing math or actively doing math and 1/2 the class period learning new math. I teach on an hour block, and do have daily warm ups and, if my pacing/timings work out, a debrief/closing. Now here’s the “weird” part:

• First half of class: Practice from previous day(s) classes.
• Second half of class: New math learning. Either from a lecture or student exploration/discovery activity.

In 2018 I finally got the chance to make it to one of Anna Vance’s Make It Stick sessions at TMC18 in Cleveland where she presented alongside my now co-worker Alli George. Their presentation convinced me that if I wanted my students to actually learn the material in my classroom I needed to make sure that I structured the learning sequence in such a way that I am actively fighting the forgetting curve.

If the forgetting curve is new for you, its basically this pretty scary looking exponential decay function that represents the amount of knowledge retained (remembered) as a function of time assuming the content is taught only one time. Here’s a graph with an x-axis that does cause some concern for a math teacher given the non-linear nature of the x-axis…but let’s not focus on that right now as the visual still gets the point across: we forget stuff pretty quickly.

And if you don’t believe that curve. Ask someone for their phone number, don’t write it down, go think about something else for 10 minutes, and then try to remember the number. You probably won’t remember the number.

So here’s the main idea between Make It Stick, and another book I’m almost done reading called Powerful Teaching:

Interrupt the forgetting curve by: Lagging (delaying) practice from when the content is learned, come back to the content often, and mix up the content with other content so that students are seeing more than one topic at a time.

Now, if you are like me in 2017 when Anna first told me that, you’re thinking, “NO WAY! That sounds miserable as a learner! They’ll never get to get into a ‘groove’ of practicing problems and they’ll be frustrated!”

EXACTLY! THAT’S THE WHOLE POINT! If we allow students to semi-forget something, have them do practice that requires retrieving that stored information from their memory and use it over and over again they will be more likely to remember it!

Back to the phone call analogy. Remember the days of analog phones? Like the pre-speed dial phones connected to the wall but new enough to have push buttons. What’s was the phone number of your best friend from those days? Funny, I bet you remembered that one! Wanna know why? Because you had to think about recalling(reviewing) the number and dialing it every time you wanted to talk to them.

Have I convinced you? If not, seriously go read Make It Stick. It changed my life and I thank Anna and Alli for that.

So that is my long-winded way of saying “here’s why we practice old material first and then learn new material second in class.”

The Smaller Routines-a.k.a. The Instructional Routines:

While routines are wonderful in the sense that they make us comfortable by removing the unknown, doing the same thing over and over again can get boring. One of the things I find most amusing about myself, and I’m going to guess this is true for you all reading this blog as well, is that I despise change, but I also hate being in a rut.

The large routine of 1/2 & 1/2 stays the same, but I like to cycle through the routines that occupy each 1/2 so that we all get a bit of variety in our lives. Here’s what I used last year:

Practice Routines as First 1/2 of Class:

I like things where the answers are either given or can be self checked so that my time is spent with students who are stuck/struggling and not with students who just want me to check their work.

• Question Stacks: These can easily be made from existing worksheets or worksheets found online. Sarah Carter (@mathequalslove) has a blog post explaining how to make them here.
• Add ’em Ups: Where you take 4 problems and format them into quadrants on a piece of paper. Then in the center you place a circle with the SUM of the answers to the 4 problems. Students can check their work easily to know if they got all the answers correct. Groups have some pretty stellar convos about finding the errors together. Sara VanDerWerf has a blog about them here. (full disclosure I found that sometimes 4 problems can be a bit much when we get into some time-consuming content, so I will do 2 or 3 problems instead)
• Partner Problems: So these have a bunch of names, and I’m not sure what you may call them. But the idea is you make a handout with 2 columns where each row has a different problem BUT where the problem on each row has the same answer. I first read about them on this blog and in finding it again to cite it I noticed they have linked to Julie Ruelbach’s rather large google drive of existing problems (SCORE!)
• Two Truths and a Lie: which I heard about from Jon Orr here and are pretty much exactly what they sound like and can be morphed into different levels of sophistication for a task.

Note that I do not grade the practice. I even explicitly tell students that the goal is not necessarily for them to complete the entire activity in the 20-25 minutes we are working on this. We WILL see the activity again (because we spiral back with our practice) so don’t worry about working quickly, worry about working accurately.

 Capstones As First 1/2 of Class:

Sometimes I want to collect work from students. Not just because I need to grade something from them (I’d love a day where I am not grading work…but today is not that day) but because I want the opportunity to give them thoughtful feedback on their work. I call these days “Capstone Days” because it means I’m going to give them slightly more time (30-40 mins) to work on a problem or a set of problems that synthesizes some learning from the previous week(s).

Sometimes I ask them to work with peers, other times its individual work. It really just depends on where we are in the learning process. If the capstone is on relatively new material I tend to let them work with a peer (but each in a different color pen) so they feel more relaxed. If the content has been around for a while I tend to have them work individually.

Here are two examples:

Note these are still just problems you could find on any existing worksheet but they’re more time-consuming so turning them into a Question Stack would just be too much. My goal for this year is to have one Capstone a week. I’ll keep you posted on my progress with that.

The Learning in the Second 1/2 of Class:

The learning part looks really different throughout the year. Sometimes it is a lecture via direct instruction. Sometimes it is a Desmos exploration activity with a debrief to make sure the whole class got the material we needed to see. Here’s an example of a geometry Activity Builder I’m really proud of that we did for quadrilateral properties to build off an activity from Michele Torres I edited for parallelograms.

Other activities that you’ve probably heard of that fit in this chunk nicely: 3 Act Math tasks,

Sometimes I have students do a Sometimes/Always/Never card sort which usually results in some nice mathematical arguments in class. We then debrief the sorts over the next day during the second 1/2 of class.

Here’s the thing I love about this structure: Let’s say you have an exploration that’s naturally a 2-part thing (when operating in 20-25 minute parts): You can do that activity over 2 days and then use the second day’s practice 1/2 to review OLDER material. It creates this natural space for older content review. Its so lovely.

 

This is the part where I admit that there is student push back to this structure over the first 3-4 weeks of class. Every year. The pushback is hard. Usually from both parents and students. I pushback with explaining cognitive science to students and to parents. This year I think I’m making an “Intro to Cognitive Science” letter to parents to send out the first week of school just to front load my reasonings. And here’s the thing. Every. Single. Parent who pushed back with me in those first few weeks, later takes it back. They see the growth in their child. The student starts to feel like the “get the math more” and begins to like the practice structures. They realize this works. And I’ll take 3-4 weeks of pushback if it means there is smooth sailing the rest of the year!

So this blog post wound up WAY longer than I had anticipated, but I hope it helps wrap your head around the 1/2 & 1/2 class structure and possibly convinces you that its a relatively simple instructional shift that yields some pretty good returns in student learning.

Desmos Fellowship Recap 1: Desmos Hacks

So This past weekend I traveled to Desmos HQ in San Francisco, California for 2.5 full days of being a Desmos-Math-Nerd with ~40 other Desmos Fellows from all around the US and Canada and another 15 Desmos Teaching Faculty and Desmos Staff. The words I can use to describe this weekend include, but are not limited to:

• incredible
• overwhelming
• anxiety-inducing
• wonderful
• exhilarating
• revitalizing

The weekend was equal parts me trying to get over imposter-syndrome/social-anxiety and me wanting an infinite amount of time so that I could talk math with my new in-real-life friends.

Because I’m way better at technical explanations in comparison to emotional unpacking, let’s start with some Desmos Hacks I discovered that were MIND BLOWING for me:

Shading Between Two Regions:

Melvin and I were tasked with playing Point Collector and we were both in the mood to try some fancy Desmos equation writing. We both were familiar with the piecewise notation for Desmos and knew that we could use the piecewise functions with some more range restrictions to create regions that would collect points like so:

BUT the problem was, for those of you who have played point collector in the past, was we needed to EXCLUDE some regions in our graph. And he and I were at the end of our Desmos rope so we did what any good digital citizen would do, we googled it*. And by we, I mean Melvin.

*Update: Melvin didn’t google, he just remembered seeing this graph.

Here’s what we found worked for us:

BUT I had no idea why this worked. I knew it did. So now that I’m back home I’m thinking and here’s what I’ve gotten so far:

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So let’s say you want to shade between two lines, the way I had figured out how to do this in the past was to write the linear equations as functions, and then on a third line write a range restriction for all the y-vales above one function but below another function. It works really well for lines, but when you get to some more complex functions or non-functions line the equations for circles and ellipses things can get tricky with my old method. My students did a lot of Desmos art projects over the past 6 years, so we’ve banged our heads into the wall in the past trying to make the image shade the way we want.

The new way: Take your equations and algebraically set them equal to zero. So y=2x+3 becomes y-2x-3=0, and y=2x+4 becomes y-2x+4=0. Then multiple the equations together and create your inequality to shade either between or outside of the two equations. (NOTE this also means if you set (equation 1)(equation2)=0 it will graph the two equations for you at the same time using only 1 line of desmos!)

Here’s an example of using this formatting for shading between an ellipse and a circle:

If you, like me, are wondering why this works, well I do not have an answer for you yet. When you have graphed something like:

(y-x-1)(y-x-5)=0 I get why you produce 2 lines. Because either y-x-1=0 or y-x-5=0 and you have those two conditions. What I’m still unsure of and thinking on is why when you graph (y-x-1)(y-x-5)<0 the area between the two graphs is shaded. My initial thinking is that the shaded area is all the ordered pairs that satisfy the conditions that make y-x-1<0 or y-x-5<0. But then I loose that train of thought when I venture out of function territory and think about the above purple ellipse and circle again.

Either way I love this new shading hack in Desmos and will continue to think on why it works.

How to Animate a Slider in Activity Builder: AKA Make a GIF without GIFmos:

If you don’t know who Jay Chow (@mrchowmath) is, go fix that right this instant. My blog can wait. Seriously, I’ll wait here while you go follow him.

Did you follow him? Good. You won’t regret it.

I’m not really sure when I first internet-met Jay, but I do know he started doing Desmos Computational Layer (think computer coding that makes Desmos ABs more fancy) webinars around May 2018 and I was super interested in learning more. So once I got over the Hawaii time is not equal to North Carolina time (I may have accidentally missed the first two webinars because I was asleep…) I started to dip my toe into CL. Here’s the first tweet interaction proof of the many ways in which Jay saves my Desmos big ideas:

Within the week he’d made an activity builder with 4 different ways to do the color code checking things of my dreams in addition to showing me a better way to do this so the function appears when the solution a student entered is correct.

So freaking cool huh? Yeah. Jay is the best.

Well while we were at Desmos HQ we had some down time to work on a Desmos project of our choosing. I decided to think on an exploration on AB that would result in students discovering the coordinate rules for transformations. In order to do this I wanted a GIF of shapes moving around the plane but ran into a problem with GIFmos doesn’t export labels from graphs. No worries. Jay can fix that.

In two lines of code he got my graph to animate. He did it using my messy pre-determined variables in the reflection slide.

The basics of the animation feature is to create a graph that has ONE slider that determines all of the movement. For the first slide that is the slider t that travels from 0<t<1.

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To animate the slide, go to the AB dashboard, click on the cog by the graph component and enter the code shown:

This slideshow requires JavaScript.

Where the animationDuration is the length of the slider (so here that is 1 because the length from 0 to 1 is one. BUT if you had a slider that travels from -2 to 8 you’d need to set animationDuration to 10 in that case).

And then tell CL which variable is the slider in the second line of code.

Easy as pi. Here’s a link to a simplified AB with the CL to grab from Jay.

Another simple thing Jay showed me was how to “turn on” the lanes of points once the transformation was over. It was so easy I’m not sure why I hadn’t thought to try it:

See those restrictions inside the points? In this slide the a-value is the slider and it travels from 0-2 to make the reflection happen. So when the slider gets to 2 the labels appear. Cool huh?

So there are my two new things I learned about Desmos from Fellows Weekend! More blog posts to come I’m sure, but for now my brain is still very confused by jet lag.

Mandatory Desmos HQ Photo:

Its Been a While

**Taps the microphone**

“Hello, Can you hear me? Anyone out there?”

**Taps Mic**

Hi y’all. So every year I have the goal of blogging more, and then every year, without fail, life throws other obligations/slightly more urgent things for me to do other than blogging. I did a fairly good job at my #Teach180 last year (take one photo from your class every day of the school year), and I hope to keep that up this year here.

As for why I’m dusting the old blog off is to recruit new people to Twitter at the M.E.L.T. conference I’m attending at App State. I’m here taking a course on Discrete Math and it is working as a crash course in all things Discrete. Some of you remember that I’ve been lobbying to end AFM and replace it with a course that is not algebra-based and more open for students of all mathematical backgrounds. WE DID IT! This upcoming 2019-2020 school year will be UNCSA’s first year of Discrete math. So like the good Twitter user that I am, the very first thing I ddi was go to the #MTBoS Spreadsheet of Classes Taught to find my Discrete people…

And I noticed there wasn’t even a Discrete Tab.

So, I then started searching hashtags. On #DiscreteMath I found mostly an unpopulated hashtag with the exception of some GeoGebra gold (pun intended) from John Golden (@mathhombre) with graph theory puzzles and fun.

Not to be dismayed I sent out a tweet:

and got some responses that I then collected in a list (that I will continue to add onto as I find more people). So now I have a new mission:

Get as many Discrete teachers online as I can find so that we have a place to share ideas, tasks, and general math fun with each other. I’m starting with the 6 lovely individuals I’ve had the pleasure of learning with and from this week at MELT.

So, if you’re new to Twitter and you don’t even know where to start, I have a few suggestions:

• Pick a handle (Your Twitter @NameGoesHere part) that you can easily say out loud or remember. I choose my name because that way people know who they’re talking to and its easy to remember if you meet me at a conference and want to tweet me.
  • Avoid a bunch of numbers, people are inclined to think you’re a “bot” and may block you.
• Profile Info add it.
  • Put a picture of yourself on there. Or your dog, your favorite __insert the thing you like__, anything. Just don’t leave it that grey silhouette of a person.
  • Put some things about yourself in the about you section.
    • What classes do you teach?
    • The hashtags you follow
    • What your hobbies are/non-math interests
    • Your website or blog (if you have one)
• Find your Twitter Friend Group. Not sure who to follow? Search some of the hashtags. The existing hashtags are aligned to the main topic standard in the CCSS as opposed to course:
  • General Math #MTBoS (The Math Twitter-Blog-o-Sphere) and #iTeachMath, #MathPuzzle
  • Algebra 1 #Alg1Chat
  • Geometry #GeomChat
  • Algebra 2 #Alg2Chat
  • PreCalculus #PreCalcChat and #PreCalChat
  • Stats #StatChat, #StatsChat and #APStatChat #APStats
  • Calculus #APCalcChat, #APCalc
  • Middle School Math #MSMathChat
  • Elementary Math #ElemMathChat
  • OpenUp Math Curriculum #OpenUpMath #LearnWithIM
    • Free online MS and HS math curriculum. (alg1/2 and geo coming this summer)
• Don’t be Shy. Okay, I get it. Engaging with strangers on the internet is a really weird concept. Most of you reading this blog grew up being told not to talk to strangers. Its engrained in our subconscious to be wary of these interactions.
  • Do more than just read tweets.
    • Scared to talk to that human? Okay, like the tweet or Re-Tweet it. This accomplishes 2 things: It stores the tweet on your like-list or timeline for future-you to use, AND it tells that person you liked their stuff and to keep it coming.
    • Ready to talk to that human? Awesome! If you see a task you like, as follow up questions. What worked well? What would they change? Were their any misconceptions by the students? If they could improve one thing what would it be? We’re on here to reflect and learn from each other. The only way to do that is to communicate with each other.
  • Share what you’re doing in your classroom. Don’t be afraid of needing everything to be perfect. The way we all make twitter a less-scary place is if people put out their less-than-perfect things as well as their perfectly awesome things. Want to see examples, check out

And if you need more reasons for joining in on the online fun, here’s my blog post from a few years ago about why I made the jump from Twitter Lurking (being a passive reader of twitter) to a Twitter Contributor (talking about math with other people and sharing things from my class) here.

Need more convincing? Okay:

• I plan my geometry course with teachers I’ve never met in real life who live all over the county and the world. We talk at least a handful of times a week. We have a google document where we put ideas for lessons. We bounce ideas off each other constantly and are vulnerable about where are weakness are as teachers and help each other in improving in those areas.
• The math family I have met on twitter have changed my life. When I found twitter I was an overwhelmed beginning teacher (BT) with no textbook, no subject-specific mentor (but an amazing BT mentor), and no idea of what I was doing. Twitter gave me free lessons filled with rich tasks for FREE. Twitter gave me a supportive professional learning network and has helped me grow into a teacher who strives to learn more from my peers.

Join me on Twitter family. Its the best PD I’ve ever had the opportunity to be a part of. There are legitimacy teachers on Twitter 24 hours a day 7 days a week thanks to our Twitter friends on the other side of the earth from where we are.

Geometric Wrapping Paper

A few days ago I posted on twitter about a project I did in geometry this year, which was unoriginally, called the Geometry Fall Semester Project- Wrapping Paper.

When friends ask for a blog post, I have to oblige. So here I am proctoring a fall semester final exam and blogging. To whom ever stumbles upon this post know that I like this project enough that I am 100% doing it next year. I also want to adjust a few things about this project because I learned a few things and think I have a way to streamline some student issues/misconceptions that occurred in the process of the project.

 

So the idea for this came to me when I stumbled across this video on the internet from SkillShare. While watching the video a million things few through my mind of possible uses in my math classroom, but I landed on turning it into the final cumulative skills task for my geometry students.

 

My geometry course starts out reeeeeaaaaally slow. Like. We have only learned the Basics of Geometry (points, lines, and planes), Logic, parallel lines cut by transversals, perpendicular line problems, transformations, and proofs of parallel line things. I spend an awful long time on proofs. I can do this because I have the luxury of teaching at a school with no state exams. Also, I have this (unproven) idea that if I hit proofs really hard first semester it will make them go more smoothly second semester (initial research seems to agree with me based on student feedback and assessments). So the final project didn’t have many skills in a list to choose from. So I opted for Transformations and parallel lines with transversals.

Students were told to create a grid via parallel lines and transversals. To find a 1″ by 2″ image to transform around the plane (translations, rotations, reflections, and dilations). They were also asked to find a small image (1/2″ by 1/2″) to put in special angle pairs on their parallel line/transversal plane (like alternate interior angles).

Once students had their main template completed to their liking with the foundation for their wrapping paper with all the transformations and small image placements where they wanted it to be we followed the video tutorial on how to create a self-repeating space. The Cliffs Notes is cut the paper in half long ways, reattach the paper so the middle (where you cut) is now on the outside and the outside edges are now meeting in the middle of the page. Add any image you like to the empty space. Repeat the process by cutting horizontally and adding images to blank space.

Here are all of my student’s designs. 

Here is the project paper I gave students. I want to re-do it for next year

Things I’d do differently/better next time:

• I need to change the wording of the handout to say that we want to create a GRID with parallel lines and transversals. This will aid in having translations that make sense if their transversals are all also parallel to one another.
• Yell from the clifftops that images cannot run off the edges of the paper you use for the template (aka the before you cut and paste the paper part of the project). This prevents decapitated Snoopy’s from repeating all over your design.
• Also yell from the clifftops that students should record what transformations they are doing AS THEY WORK on the template. Its really difficult to remember what you did three days after you drew it.

Anyways, I hope you like the project. Let me know what recommendations you have for improvement or if you use it and make it better.