M&M Lab

Advanced Functions and Modeling is an alternative to PreCal course. And this year I choose to move the Descriptive Stats unit from the very first unit in August to the first unit of the second semester in January. Our Stats unit is very simplistic as it is meant to be an introduction of sorts. Tt contains the same content from CCM1: Measures of center, calculating 5-number summaries and outliers, creating histograms and box plots. We choose to have the unit focus on arguing with data rather than purely analyzing data.

Arguing with data, for the purposes of the class is when students are given data, a side-by-side box plot, or multiple histograms on the same scale and then they need to:

  • Make a claim–students need take a stance for the data given. We modeled these statements to reflect the thesis statement construction from their US History class (which most students are in).
  • Provide three supporting statements for the claim. Each statement should be data driven and assist your claim.

The Lab was inspired stolen from an image I found on Twitter. I can’t find the source, most likely someone in #MTBoS.

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And I figured this was a lab that could be easily recreated for my students. I, with the help of my loving husband, created “Mystery Morsel” packs. We created packs made from large index cards that we put 5 M&Ms in and sealed. We made 7 packs for each type of M&M.

Students were tasked with identifying the “Mystery Morsels” by using their weights. Each group was given a control baggie of M&Ms to come up with a baseline for each type. They shared their data on the board for weights of their M&Ms and then proceeded to weigh the “Mystery Morsels”:

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Was it a perfect lab? Heck no. I think it was far too easy and there are many things I want to change for next year. Several kids noted that “it was obvious” which M&M goes to which pack because the weights are varied. One student mentioned that it would be “evil if Mrs. White hid skittles in here somewhere. I bet they weigh about the same as the plain ones.”

Which got me to thinking…skittles…yes. And Reese’s Pieces. And maybe one random packet that has 6 M&Ms instead of 5.

My rational for this “trickery” is to have some of the box plots overlap in the range of the data. So students actually have to use their knowledge of measures of center/variability to rationalize their decisions for which of the “Mystery Morsels” belong to which M&Ms and which are “other” candies.

 

Lab handout

Week 1 in Review

This year marks my third at UNCSA and I have never looked forward to, and dreaded, the start of a school year so much. I’ve had the pleasure of staying at home for the past six months since the birth of my daughter. That being said, I am not cut out to be a stay at home mom. I’m not organized enough, I’m not good at keeping my brain engaged and working, and I developed a bad case of cabin fever. So in one way I was REALLY looking forward to the start of the 2016-2017 school year. But I dreaded the start of the year because I have felt behind since August. I didn’t get the lesson planning done during maternity leave I (naively) had promised myself I’d do before my daughter started daycare. I haven’t spent the time I feel that I should at home lesson planning because I’d rather be holding my girl and planing peek-a-boo (do you blame me?). And as luck would have it, she got an upper respiratory infection the week school started, so I’ve spent the past few nights up at all hours rocking her to sleep, which left me no choice but to be highly caffeinated to survive the teaching day. I have never felt so shaky at the beginning of the school year, but I think I did do a few things right (or at least I am calling them a win) from my maternity leave to-do for the 2016-2017 school year:

Get better about learning names:

I used Sara VanDerWerf’s Name Tents to aid in both the learning of my students names, and in getting to know them a little better within the first week of school. It was the best decision I could have made, I may never have to try another way to learn names. It was super awesome to get the chance to have a private conversation with each student. They kids responded to the prompts:

  • What do you want me to know about you?
  • Give me your 6 word math memoir.
  • What’s your favorite thing to do outside of your art area? (I teach at an arts school)
  • Doodle me something about yourself and explain the significance.
  • What is your most vivid mathematical memory?

My favorite was the doodle, you’d think that in a classroom with a few visual artists and a ton of dancers, musicians, and actors that the kids might be shy on doodling. Nope. I drew them a picture of my stick figure family on the screen with the prompt, so I set the doodle-bar kinda low intentionally to set their minds at ease.

Don’t go Over the Syllabus in Class

Some where along the line, someone told me to go over the syllabus on the first day. That it sets expectations/demonstrates norms/ya-da-ya-da. I hate syllabus day. Even last year’s attempt at making it bearable (each slide had an internet meme and/or GIF), you know the ones:

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But it was painful, the kids stopped listening 3 slides in (once I was done talking about my story and started talking about “class rules” kinda things). So I ditched it. My syllabus lives on Canvas, our online learning platform. My students are all sufficiently good enough readers to handle reading it on their own–with the exception of a few ELL students who I made time in the first week to talk to about the syllabus to ensure they were up to speed. So my first night’s HW assignment was to read the syllabus and to take my online Student Information Quiz (in Google Forms format). Students then logged into Canvass and posted three questions they had regarding the syllabus in a discussion forum, and answered one peer’s question. I addressed any further concerns on the second day of class and it took less than 10 minutes. Win!

 

Focus on Group Dynamics, Not The Math

I know, I know. “You’re supposed to do Math on the first day” to set the tone for the year. Yes, I agree, but I wanted the focus of the first week of my class to be on the group work dynamic so that when we step up the math, they are already comfortable working in groups. The first math problem I did with my students I sawn on Fawn Nguyen’s blog that she got from Don Steward:

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The problem was more successful as a day 1 task in my PreCalculus and Advanced Functions and Modeling classes than in my Algebra 1 class. But they all had some pretty stellar math talk going on and eventually (with differing levels of hints) got the final answer. On a related note: America needs to get on board with the metric system.

Day 2 we did a task I first read about in Designing Group Work and Sarah Carter was so kind to provide already made up on her blog: Rainbow Logic. The idea is that the students use strategic questioning to infer the color pattern on a peer’s tic tac toe board. The kids got WAY into it. I should have taken pictures, but several groups were convinced that their facial expressions were giving away information, so they hid behind the file folders I gave them to separate the “game keeper” from the players. We did four rounds of the activity. Three of the rounds were with 3 colors and the last round was with 4 colors. So far my students record for number of questions to get the correct color combination was three.

  • They asked for the first row’s colors
  • Are there more than two of each color in any given row?
  • Is the center color blue?

I didn’t witness the whole thing go down. But I am to understand that there was an educated guess on one square placement that yielded success.

 

It was a good first week. And it only took me until half way through week two to get around to reflect on it…

I Have a Plan: Cleaning Up My ‘Dirty Words’

Julie (@jreulbach) is awesome, but I’m pretty sure anyone reading this was already well aware of that fact, and has gathered all of the Algebra 2 teachers of the internet to join together in a blogging initiative. While I’m not teaching Algebra 2 this year (I had to give it up in order to get a first period planning in order to have a little more flexibility in the mornings with getting my 6 month old daughter to daycare), I am teaching Advanced Functions and Modeling. A course which is currently Algebra 2 version 2.0 for most portions of the curriculum. There is little to no new information presented to students, and most of the current design has a computational focus instead of an interpreting and analyzing focus. As the course is designed AFM is meant for those students who need a math beyond Algebra 2, in order to be college competitive, but who aren’t ready for the rigor of PreCalculus.

AFM’s current course description:

Advanced Functions and Modeling is designed to further strengthen algebraic manipulation and graphing skills while introducing a selection of other topics and application. Additional topics may include trigonometric functions, sequences and series, and probability. Concepts will be applied to real-world situations and technology will be used regularly. Prerequisite: Algebra II

I inherited this course description and a problem set/note packet for the course from my coworkers. While I am not a huge fan of the layout, mostly because it follows the Alg 2 curriculum very closely, I have just now had time/energy to try a re-write.

The old curriculum mapping went:

  • Introduction to Statistics (measures of center, spread, comparing data, and normal curves)
  • Linear Functions
  • Quadratic Functions
  • Transformations
  • Exponential and Logarithmic Properties and Functions
  • Sequences and Series
  • Trigonometry (Triangles and Functions)

Given that students I teach in AFM are the same students who struggled with Algebra 2, this ordering has never felt 100% right to me. If they struggled with Algebra 2 material when it was in Algebra 2 is it really effective to just re-package the same content in a new course and call it AFM? I understand the need for students developing an actual understanding of key material from Algebra 2, especially if we want them to go on and be successful in any math classes they may take in college, but I wasn’t okay with presenting the material in the same way they had seen it before. As compartmentalized chunks of math that are always taught in the “here’s the rule”, “now here’s the practice”,”now here’s the ‘real world’ applications” structure. After much #MTBoS lurking during the first 6 months of my daughter’s life/my stent as a Stay at Home Mom, I think I’ve found a sequencing that I can finally support. Shout outs to Mary Bourassa’s blog for giving me the spiraling content idea.

  • Unit 1: Introductions to Functions— functions vs relations, function notation, domain and range, family or functions.
  • Unit 2: Introduction to Modeling— a mixture of Linear, Quadratic, and Exponential functions. The focus will be on justifying the choice of a function as a model for a given situation (from a table, graph of points, or verbal description)
  • Unit 3: Introduction to Statistics–Reading tables (%s), Measures of Center, 1 Variable statistics and data visuals, Normal Curves and z-scores, and for the first spiral: Regression (linear, quadratic, and exponential).
  • Unit 4: Transformations of Functions— Spiral from Unit 1 with a lot of Domain and Range descriptions. I know I’ll do a few Marbleslides in here.
  • Unit 5: Sequences and Series— I will start of with Visual Patterns as an informal “find the pattern that works and prove it” exercise, and then move into a more formal definitions of arithmetic and geometric sequences (spiral from Unit 2 with Linear an Exponential)
  • Unit 6: Geometry— I’m still in the brainstorming mode for this one, but I know I want right triangle trig in addition to some review from their Geometry course. I have been told by the SAT prep teacher that the geometry sections of the SAT are more rigorous than in the past and that my kiddos will need the refresher. I would like to bring in some of the IB Math problems I did at my old school, they were really good for getting students to think outside of the box and talk about the math.
  • Unit 7: Trig Functions— Focus on using information about a situation to create a function to model the situation (max/min values and period), spiral with the transformations unit.
  • Unit 8: Financial Math— A good portion of my students are seniors who go straight to a dance company, music chamber/conservatory, or the work force, instead of college. So they need a crash course in how to ‘Adult.’ I have talked about credit cards, monthly budgeting, leasing-vs-buying a car among other ‘adulting’ topics.

So far I’ve only made it through actually planning half of the first unit. I’m trying my best to move away from the “I do, we do, you do” style of teaching of the materials I inherited. Last year I didn’t change them because I knew I’d be out for half the year on maternity leave, I didn’t want to rock the boat and cause a headache for my maternity leave sub.So, I fell into the habit of drill and kill style instruction. I hated it. The students hated it. I don’t think they had any ‘ah-hah’ moments with the curriculum, and most importantly, I don’t think I changed their mind on math. Math was still hard. Math was still boring. And Math is nothing more than a combination of formulas you’re supposed to remember.

That is not the math classroom I want. In the past I have taken great pride in taking the students who hate math, and through modeling and problem solving activities, I slowly changed their hatred to mild distaste. Which for the time span of one school year, I’ll consider a victory. I, for selfish reasons, shifted my focus in my classroom and I need to get back on track. So I promised myself I’d do better by my students this year. I’d make worksheets/kill and drill practice a dirty word in my instructional vocabulary. I need to get back to my instructional happy zone: using math to ponder our world, model things we see happening, and answer questions we have about our surroundings.

My goal for this year is to have one day of instruction, some of which will be self guided, discovery style learning, and other parts will have to be direct instruction because I haven’t found a better alternative yet (let me know if you have one, until then part of my instruction will have to be the well timed curse word in my dirty word worksheet world). The instructional day will be followed by hands on practice, some sort of combination of Desmos activities, group activities, and 3-act problems/labs. I’ve found a bunch of interesting problems thanks to #MTBoS that I plan on using and/or altering to suit my needs to achieve this goal. Fingers crossed I can help improve my potty mouth. Both figuratively speaking with the change in instructional practices, and literally. I’m not cut out to be a stay at home mom, and my boredom did lend to a rediscovery of my love for colorful language…I need to work on that s*@#t before my daughter starts to pick up words…

Goal Setting

Okay, I’ll be the first to admit. I’m god awful at setting routines. I thought to myself approximately 6 months ago, as I sat on the sofa 41 weeks pregnant trying to convince my daughter to make her grand entrance to the world, that I would be ‘productive’ during maternity leave. What’s that? Did I just hear the collective mothers of the internet laugh at me? Yeah, I was naive and operating under the misguided belief delusion that I would get some school work done while lil one slept. Fast forward to present day, and I’m one week away from the official start of the school year. I need to get my act together. Lil girl is in daycare two days a week, so I want to utilize this baby-free time effectively and set up some routines for the 2016-2017 school year.

My goals small, all things considered. I will have, in essence, three new preps this year: Algebra 1, PreCal, and Advanced Functions and Modeling. While I’ve taught AFM before, I am redoing the curriculum. Trying to officially make the move from Algebra 2 2.0 to a unique course that prepares my students for either college level math or the real world, depending on their plans post high school. My math department has decided that PreCalculus needs an overhaul (I agree with this sentiment) to better align with the PreCal topics taught in other (read: Traditional) public high schools in the state. And I haven’t taught Algebra 1 since my student teaching days. Bearing that in mind, for the 2016-2017 school year, I promise myself that I will:

Promise 1: Actually use a paper planner to record thoughts/deadlines/important dates

I tell myself every year that using the calendar app on my computer is sufficient. Its not. I never go back and look at the notes I leave myself because, well, its just too tedious. I have to remember what day I taught what, and then double click, no wait, wrong day…scroll…scroll…what was I doing again? So after much thought, and finding the concept of a Bullet Journal online, I have created my own planning template. Inspired by a tweet from @mathequalslove I just placed the online order to have it printed up on nice paper and bound at Office Depot. I figure if it looks nicer than what I could do with the copy machine at school, and not in a 3-ring binder, then I will be more inclined to use it.

The planner starts with the a year overview. A place where I can write down important dates for the school year like faculty meetings, math department meetings, exam days, and holidays.

Planner. Year Overview

I’ve then got a weekly overview for each course. My math department likes to use this table-format for pacing purposes from year to year. Since we all switch courses so often, it is a courtesy to a future teacher of the course with a general guideline for the year. Because we are in North Carolina, and an inch of snow will cause sheer panic and destroy any pacing template I’ve done in the past, I decided to make my pacing guide big enough to fit Post-It Notes Page Markers so I can move topics around without the need for white out/an eraser.

Course Pacing

And then I have a weekly lesson planning section where I can put in more detailed notes about the day’s lesson, what went well, what I need to fix, and what plans I have for the next time I teach the topic. Consider this section a place for mini journaling (which will help me with my next promise). I decided to leave the section for the dates at the top blank so I can use the same template year to year without the need for editing. Also, it is WAY cheaper to get a black and white cop of the planner made, and I have plenty of pretty colored pens that will add the date nicely!

Weekly Planner

Then the attendance sheets

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Files: Attendance Sheets, Planning Template

 

Promise 2: Become a Blogging Member of #MTBoS

I think it was Sam Shah who posted about the types of #MTBoS participants. I have fallen into the category of ‘The Stalker’. That is to say, I read a LOT of blogs by MTBoS tweeps. I steal borrow a LOT of their lesson ideas or handouts. I mean half of my interactive notebooks for Algebra 2 last year were inspired by Sarah Carter’s (@mathequalslove) notebooks she posts about. Not to mention my, hands down, favorite end of the year lab for AFM which I outright copied the concept for from Jon Orr. His CSI Crime Scene Lab was such a great idea, one I couldn’t dream of having, that I couldn’t resist making my own version of the hook video.

When I read about all the wonders Desmos had created by adding the Activity Builder feature I could resist and had to try it out. With some success, and failure (earlier blog post). I think I audibly giggled with delight when I got an email from the, one and only, Dan Meyer asking if Desmos could use a version of my activity. *Swoon* #MathBloggerIdol

Desmos

So I started dipping my toe in the #MTBoS water this summer. Replying to some tweets. Joining in a few conversations. Testing a few Desmos Activities when asked and providing feedback. But I’m ready to take the next step: I’m going to promise myself to blog at least once a month. I have been hesitant to blog about my lessons in the past because I’ve felt like they aren’t worthy of the #MTBoS. I mean, I’m relatively new in the game of teaching, and my lessons aren’t all something to write home about. But a thred I read from Dan and Meg Craig really stuck with me:

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So here I am #MTBoS. Ready to start blogging!

Promise 3: Have first semester planned out by the start of school

This is my slightly unrealistic goal, but I’m trying to set my goals high, well at least for the two courses I am sole responsible for: Algebra 1 and AFM. I’ve already paced out the first semester of AFM and started on the notes packet for Unit 1 (Prerequisites to Modeling with Functions). And I’m hopeful that I can reuse most of my departments resources for Algebra 1 this year. So if I use the next 15 baby-free days (thanks to Daycare!) between now and the start of school. I hope I can get this done!

That Time I Face Palmed in Algebra 2

It has happened to us all. You have a great idea, scratch that, you have a WONDERFUL idea. An idea for a lesson/activity/warm up that you are so stoked about sleep is difficult the night before. And then, during class, that idea falls flat. So flat that you’re not even sure it has a cross-sectional area. It is the definition of a line with a slope of zero. It hurts. So I’m not going to say this this lesson fell that flat, but we’re talking a slope of 0.125 (1 out of 8 kids understood the task at hand).

The Original Task: Desmos Activity Link

The stage for the activity had been set the day before. We had spent the day reviewing how to write the equation for a linear function when given either a slope and a y-intercept, a slope and a point, or two points. The kids seemed to be on top of it. The exit ticket I did had 95% of the class able to do all three. I knew I wanted to try the Desmos Activity Builder that week in class. So I figured I’d give it a shot. The goal of the activity was to have students, while working in pairs, learn how to use Desmos while demonstrating their ability to create the equation of a linear function when given some basic information. The activity then ended with asking students to recall the concept of Domain and Range from the previous chapter to draw one of the letters of their initials using linear equations and domain restrictions.

The concept was okay, the scaffolding was NO WHERE NEAR what it needed to be. The things that I did wrong/the universe did wrong with this first task:

  • I introduced too many new things at once. It was our first day using the iPads (new tech for some of my kids), it was our first Desmos Activity, and it was the second day of writing linear equations.
  • The Wifi hated us. The school had just upgraded a server (or something like that…I don’t speak IT fluently) and had inadvertently kicked everything Mac related off the network. I had noticed I lost printing capabilities earlier in the week, but didn’t think to check the wifi status of the iPads before beginning the activity…oops. The students weren’t able to stay online for more than 3 minutes at a time and they only had access to the guest network which was running slower than molasses.
  • I didn’t set my expectations for their behavior during the activity. What to do if you’re stuck (ask someone else first), what to do if you understand and want to help someone, who to let me know you’re hopelessly lost and need me ASAP.

Fortunately, this mess up of mine was on a Friday. I had all weekend to think about what to change about the activity and how to make amends to my students for causing them a 40 minutes of on-again and off-again frustration. I decided to keep the Desmos Activity platform, but to upgrade a lesson from my early days of teaching: Linear Putt-Putt to an interactive experience. I had written down comments students had made, constructive and otherwise, from the failed activity and tried to do better.

The Upgraded Activity: Linear Equations Putt Putt Desmos Activity

Linear Putt Putt Screen Shot

The idea was to give students 4 holes on a putt putt course with a variety of obstacles in their way. Students would need to create 3 linear equations (for a par 3 course) to successful navigate the course and end with a line through the hole. Students were to use domain restrictions to ‘cut off’ their lines so that they represent the path of a ball for each putt. We assumed that the balls would stop where the domain restrictions stopped (I would love to extend this activity one day to have actual angles of impact hold true for hitting a side wall…but we didn’t have time for that).

The things I changed from the Original Activity to the Putt Putt Activity:

  • I apologized for throwing too much at them. I realized, in hindsight, that we needed to move slower. I think that this threw a lot of my students for a loop. I think that they had never heard a teacher apologize before, but I asked for forgiveness for the frustration I caused on Friday, and their promise to wipe the slate clean and try a new activity. They agreed and we moved on.
  • I gave the students two movable points that they could drag and drop wherever they desired. One point was the ball, and the second point was the “ending” point for their putt.
    • This gave students more confidence in creating a linear equation. I heard on Friday’s failed day “HOW am I supposed to GUESS where a line is? I’m not a mind reader! UGH.” on more than one occasion. They had a point, you can tell a student to create a letter on a piece of graph paper because they can create the points that restrict the line…but on an iPad, that simple task is made much more difficult without the use of draggable points.
  • I made the points restrict to whole numbers. I’m not against equations being messy, but I was trying to build their confidence, not crush it again. I wanted nice whole numbers for them to play with so that they would feel less intimated by the new online resource.
  • We completed the first hole TOGETHER, as a class. I called on students to tell me where to drop the ball, where to move the second point. Then we calculated the slope between the points and created a line together. A student then pointed out how easy it would be to restrict the domain “since we know the x-values for both of the points!” I had her come up to the computer and show us how to restrict the domain using Desmos. We did the same for the remaining two lines and talked about strategies for completing the remaining holes.

Alg 2 Linear Equations Putt Putt

This went leaps and bounds better than the first activity. Students were engaged, they were trying to complete the holes under par in order to have a ‘better putt putt score’ than their neighboring peers. I even heard giggling this time around. We had great whole-class conversations about how you would draw a vertical line with Desmos (we had not yet talked about the equations for vertical and horizontal lines). There was even one student who was so intent on having his lines follow the “true trajectory of the ball” that he was googling angle of impact and trying to figure out how to get the slope he would need to have the ball “bounce” off a wall and keep on going so that he only used one stroke instead of two. He opted to use perpendicular lines to represent the bounce, and quickly realized that his method didn’t reflect the real world physics of how a ball would bounce, but he did manage to make a hole in one on the first course using his method. So I’ll call it a win.

The Moral

Some times your intentions are wonderful, but your execution needs a little more work before you unleash an activity on the kiddos. A special thanks to Desmos and the #MTBoS community for taking a look at the Putt Putt activity before I presented it to the kids and for the invaluable feedback that made the activity run smoothly the second go round. Y’all rock!

Teaching Philosophy Ramblings

Now entering my second year of teaching at my new school, I am in the process of submitting a portfolio for my contract renewal (3 more years). Until now, I’ve never had to actually sit down and write an honest to God teaching philosophy. We discussed the concept in my MAT program, but I don’t remember ever really typing out what I thought about teaching–then again, I’m not sure what I could have said about my teaching philosophy with 0 hours in a classroom under my belt back in the day. So today, I present to the internet-world, my Teaching Philosophy and Self Evaluation statements for my contract renewal. I felt it was important to share this as I attempt to enter the #MTBoS world of putting my teaching life out there on the world wide web 🙂

 

Philosophy of Teaching Statement

I spent the vast majority of my educational career telling myself that I was never going to be a teacher. Math was a subject that never really came ‘naturally’ to me while in primary and secondary school. I always enjoyed the puzzle-like nature of mathematics problems, but I was never good at memorizing algorithms for completing math problems—which was the instructional method implemented by the majority of my teachers at the time. I decided to study mathematics in college with the intent of going into logistics or some other similar field, but never dreamed that I would one day become a teacher.

That changed when shortly after college I joined the Peace Corps and spent twenty-seven months serving in the rural foothills of the Andes Mountains in northern Peru as a Community Health Volunteer. My town was small, with no electricity, no telephones or cell phones, minimal access to running water, and limited vehicle transportation. My town was not the ideal location for young Peruvian teachers starting their career. We didn’t get the committed teachers, the ones who would stick around to inspire young minds. Instead, we got the teachers with the lowest test scores on their national exam and the least interest in the teaching and learning process. Three teachers left the town two weeks into the rainy season my first year in town, which coincided with the second month of the school year. Shortly afterwards the parent’s group contacted me with a simple request: to teach 3rd grade mathematics at the primary school. I was hesitant to agree, my Spanish was limited to health topics and small talk, not the mathematical language needed for teaching, but I agreed to teach for a few weeks, just until their teachers were replaced. Next thing we all knew, I was finishing my Peace Corps service having taught mathematics and science to my town’s youth for two years. We learned about addition and subtraction by running a small business selling snacks with a local storeowner. We studied multiplication, ratios, and areas of shapes while designing houses for our student’s families and creating murals to paint around campus. It wasn’t traditional teaching…I knew I didn’t want to do that…but my students learned math while learning about life – and in the process I found my life calling, to teach.

I first learned the pedagogical term for the type of mathematics instruction I used in Peru while studying at Duke University to earn my Master of Arts in Teaching: Project-Based and Problem-Based learning. The idea is to use real world context to teach mathematics by focusing less on the mathematical theory that persists in the traditional direct instruction methods of teaching and shifting the focus to applications of mathematics with hands on activities. I have bounced back and forth from full-scale implementation of the Project-Based Learning curriculum to a scaled back combination of problem based learning with direct instruction over my teaching career.

I have come to believe that mathematics is best taught through its applications, not as a set of rules, regulations, and restrictions that are to be memorized and then restated. When students are given the opportunity to model a real world situation with mathematics they are more likely to retain the information being presented rather than learning the material in a traditional algorithmic method. With this in mind I strive to create student centered learning tasks such as labs, engaging problems, and projects, in which students need to utilize the mathematics they know to argue a point or to create a hypothesis to be tested. A mathematics classroom should look a lot like a science classroom—students should work in groups, create and perform experiments, test hypotheses, and interact with the math they are learning.

Self-Assessment

In my first year of teaching at UNCSA I made the decision to integrate student-centered problems, period-long group tasks that tie together short sections of direct instruction, into my teaching practices. This decision was partially driven, or at least sustained, by my involvement with an online mathematical professional development group called the Math-Twitter-Blog-o-Sphere (#MTBoS on Twitter). The MTBoS brings together math teachers, district-wide curriculum coordinators, technology developers, and instructional support staff from around the United States and the world.

I discovered that most of the students whom I teach at UNCSA are math-phobic; they have spent a fair amount of their academic career either feeling as though they are not good at math, or earning grades that would make them feel so. I noticed in my students last year a hesitation to participate in class, resistance to voice an opinion about an answer or to even make an educated guess as to where to begin a problem. I believe that this shyness stems from a feeling of never being “correct” while in a math classroom. I noticed that the same students who were quiet and reserved in math were outspoken and opinionated in their social studies and English classes. The MTBoS had suggested over the summer that perhaps this math-phobia could be eased by providing students a safe start to every class period – A question or discussion topic that has multiple entry points, or easy access for all skill levels, and that most importantly, that don’t have a correct answer.

So this year I made the decision to introduce several types of warm ups with no correct answers that would easily generate discussion and constructive criticism in my classroom. To start some classes we will do a Which One Doesn’t Belong? activity where students are given 4 images, graphs, numbers, or shapes, and they must give a reason for why each image does not belong to the entire group. We then spend time elaborating on student responses and increasing the amount of mathematical vocabulary utilized to justify their responses. I have noticed that even my weakest students, the ones with the least self-confidence in math, have the most unique answers for these warm ups and are usually the first to point out a reason for their argument. Other days in class we use 1001 Math Puzzles, an online resource of non-grade specific brainteasers and logic puzzles, where students are asked to visualize shapes and colorings or objects to make an argument for their rationale in answering the prompt of the day. Every Friday we play Set, a math game in which students are given 12 cards and asked to find sets of 3 cards that meet a specific set of criteria. Even though we are only 2 months into the school year, I have seen a huge improvement in my students’ willingness to voice an opinion, mathematical or otherwise, growth in the ways in which they describe and argue with mathematics, and a higher overall sense of confidence while in the classroom. I look forward to continuing this practice over the course of the school year and hope to continue to see improvement in students’ willingness to participate and an increase in the mathematical vocabulary utilized when making an argument.

This year I have also used a variety of new online technology resources in the classroom, such as the Desmos Activity Builder, to integrate formative assessments into my weekly instruction. This tool allows me to create an interactive iPad task for the students to work with where I can see their work and provide feedback as we move through a chapter. Recently I vetted a Desmos Activity that I created to the MTBoS community and received invaluable feedback as to ways to improve the content of the activity and to differentiate the activity to suit a variety of learning levels. The lesson was a huge success not only in terms of the content in which students demonstrated mastery, but also in the engagement level of the students. I am currently working on integrating the use of iClickers, a student response system, into my classroom as well. This will allow the collection of formative assessments to gauge students learning throughout a class period through the use of multiple choice or matching style questions. I plan to have the iClicker system up and running in my classroom by fall break at the latest.

In addition to these new warm ups and instructional resources, I also created a new non-routine problem or lab to every unit in my classes this year. The math department decided to introduce non-routine problems into the PreCalculus curriculum in order to better prepare students for AP Calculus. These problems are somewhat open ended, related to current and/or past content, and intentionally worded differently than other problems from class. The idea is to give the non-routine problems to groups of students and to assess, utilizing a department created rubric, how they handle the problem in terms of group collaboration, mathematical language utilized by the group members, content cited, and problem solving methods used by the students. I have decided to introduce these non-routine problems into my Standard Algebra 2, and AFM classrooms, to assess the critical thinking skills of my students. I hope to see them succeed in these problems with the confidence they seem to be gaining from the non-math warm ups this year.

I am currently in the process of redesigning the Algebra 2 and AFM curriculum to better meet the needs of our students. Currently that involves shifting the focus of a few units and the sequencing of the year so as to stay within the current course descriptions for both courses. I look towards next academic school year, however, I would like to propose a major overhaul of how we treat the AFM class at UNCSA and what standards we cover as a course. With its current focus as written in the course description, AFM is a repeat of Algebra 2 with an increase in the amount of hands on activities and labs that students perform. I feel that we would better serve our students if AFM provided the opportunity for our weaker math students to explore new mathematics. For instance, there is a topic in number theory, called modular arithmetic, that is the foundation for how credit cards, ID key cards, encryptions on your email, and how your personal information is transferred over the web, which can be explained using basic arithmetic and understandings of functions. That is to say it is accessible to students who can perform basic arithmetic operations such as addition, subtraction, multiplication, and division, but separate from the curriculum they have already been provided while in Algebra 1, Geometry, and Algebra 2. While a sophisticated application of mathematics, the security of your information is not rooted in the complexity of the mathematics involved, but rather the tedium of calculating the products of very large numbers. The concept of how to securely design encryptions to protect your information on the web is well within the grasp of our students’ abilities and could provided an interesting shift in how we view an upper level math course at UNCSA that is not on the AP curriculum path. I feel that the shift away from the repetition of Algebra 2 with AFM would not only increase the mathematical confidence of the students, but vastly improve their reasoning skills and problem solving abilities—both of which are key to success not only in college and beyond, but for the preparations for college like the SAT and ACT. I would also like to have students modeling with combinations of linear, quadratic, exponential, and trigonometric equations from the beginning of the year with the use of a graphing calculator or online calculator rather than waiting until after an in depth review of Algebra 2 so that students would solve the equations by hand. It is my belief that students in a course such as AFM would benefit more from the critical thinking and problem solving skills required for modeling with combinations of functions than the process of using algorithms to solve and create these equations by hand.

It is my hope to have a newly drafted AFM curriculum to present to the Educational Policy Committee by fall 2016 with the hopes of introducing the new curriculum changes in fall of 2017. I want to redesign the course with the input and feedback of my peers to create a course that pulls the focus of AFM from Algebra 2 and moves towards new math for the students to explore that will meet the requirements for admittance to university of a math beyond Algebra 2 to ensure that AFM students are eligible for college.

New Year, New Routines

I teach at a residential high school for gifted young artists. They leave their homes, their former high schools, and their friends and travel to Winston-Salem NC where we have the pleasure of teaching some of the most talented young dancers, musicians, vocalists, drama performers, and visual artists from all around North Carolina and the United States. In addition to a full academic work load (the usual math, science, history, and English classes from any other high school) my students have the added responsibility of taking a rigorous college-level art classes alongside their peers from the University and Graduate programs here on campus. They have a lot on their plate.

This year I teach standard Algebra 2, Advanced Functions and Modeling (an alternative to PreCalculus for students not looking to go onto AP Calculus), and this year I have a PreCalculus (but won’t next year). Last year I only had Algebra 2 and AFM, and I noticed a hesitation among my students to put them selves out there mathematically. The classes I teach tend to have the more mathematically fearful students in them: the 11th and 12th graders in Algebra 2, students with lower math averages in previous classes, and a fair amount of mathematical baggage from their previous high schools. Every year I have them write a math bio. An account of what they remember liking/disliking in their math career, what they are amazing at, what scares them, what they are most concerned about with math this year. It gives me a lot of insight into the teenage minds:

“I have always been bad at math and have never felt like a teacher really cared enough to explain it to me.”

” Math has never made sense to me.”

So I have a lot of mathematical damage to repair. I have two goals for myself this year in my classes, in order:

  1. To increase students engagement in and willingness to try mathematical tasks.
  2. To teach the material in a way that students retain the information.

Goal 1: to increase student engagement in and willingness to try mathematical tasks.

So, to work towards this goal I introduced the “non math” warm up. Thanks to the #MTBoS tweeps I have stolen borrowed some great warm ups with a focus on critical thinking, math talk, and problem solving.

  • Every Friday we play Set.Today's Daily Set 9/11/15 A mathematical card game available online (I take a screen shot) in which you need to identify a set of 3 cards in which the characteristics of the shapes are either all the same or all different. Today the first two sets my first period AFM found were the grey set (all the same color, all different numbers, all the same shading, all the same shape) followed by the yellow set (all the same color and number, different shadings and shape). It took 4 weeks for them to 100% get the hang of it, but I love the culture it is forming in the room. Kids are talking to each other before putting their guesses out there for the whole class to critique. We are having constructive criticism of “wrong” sets and helping their peers adjust a set selection to then have a “correct” response. Its also a lot of fun to see them enjoying my favorite nerdy math game!
  • Which One Doesn’t Belong? WODB?I had the pleasure of meeting Mary Bourassa this summer at Anja S Greer Math Conference up in Exeter, New Hampshire. I fell in love with the simplicity of the task and the multiple entry points for students. We are starting off the year with the shapes and numbers categories and will move into the function options as we move through the year. My favorite WODB is to the right. In my lower level classes students found differences with the shapes of the letters, “K is the only pointy line segment one” or “P is the only one without a lower half.” Not ground breaking, but still awesome. Then my upper level PreCal students took the floor with “K is the only one that doesn’t end in a eee sound. Pee, Bee, Dee, Kay.” Oh man, now we’re getting deep. “B is the only even numbered letter. Like if you assign the letters numbers 1-26, K is 15, P is 23, B is 2, and D is 5.” I had a huge grin on my face for the rest of the period because I didn’t even go that deep with the warm up when I was playing along. I love it!
  • Because I teach a students with very strong passions and opinions (which I adore) they have the  most fun/arguing potential with Would You Rather… A picture prompt that has students building an argument (mathematical or not) for why they would prefer to do option A over option B. We have started the year out with allowing for non-math answers like “80 bars of soap would fit in my book bag but 30 towels totally would not.” But we will move into the more mathematically based opinions as we progress through the year.
  • Then I also pick a random problem from 1001 Problems to work on visual problem solving. Hole PunchOut favorite from the year has been the Hole Punch Problem. If you make the indicated blue folds, then use a one hole punch on the indicated black dot, what will the unfolded paper hole pattern look like. This was a great experience for my kids visualizing the number of layers in the paper underneath the hole punch. Some even got out scrap paper and were poking holes in it with their pencil.

Goal 2: To teach the material in a way that students retain the information.

I wish I could say I have found the silver bullet for this problem, but I’m typing this blog while one of my classes takes a test, and I can tell by facial expressions alone we’re not there yet. Either way–the things I have changed this year:

  • I will always, ALWAYS, post answers to HW assignments the night they are due on Blackboard with the understanding that students will check HW answers prior to arriving in class (I never give more than 5-10 problems) so that we can spend a few minutes post-warm-up to fix any issues/concerns they have. My hope is that this allows students to catch “silly” mistakes and we can spend time focusing on the real underlying issues/tricky problems from the night.
  • In Algebra 2 I am testing out a hybrid of Guided Notes, a system I have used for most of my teaching career as I find that it allows for more time to work example problems if the students aren’t writing so much, with Interactive Notes. I have been following Sarah Hagan‘s blog and twitter (@mathequalslove) for a few years and have been meaning to try her interactive notebook idea but never had the motivation until this year. The students so far seem to enjoy them, but we are still working on convincing students to use their notes as a primary resource for helping them through an in class assignment–rather than asking me first. It is a process, so I will keep you all updated. This is definitely my work in progress project for the year. Learning as I go.
  • Increase the number of labs/hands on activities that I do in each unit. I am making time for 2 labs per unit so that students can connect what we are learning with applications and trying to work in more manipulative activities.