Category Archives: Curriculum

Reflections on Curriculum Implementation, Week 5

My district just finished our fifth week of school. This year we adopted a new math curriculum that I am really excited about, and I wanted to write a bit about my experience so far, partly so I can process, partly so I can remember later, and partly because I might be using this information in my final project for my Equity and Social Justice class I’m taking for my master’s degree.

First, having a curriculum at all is a huge change over our previous arrangement, where we basically didn’t have anything. Our previous “curriculum” included a curriculum calendar, descriptions of standards, and a wiki site where others using the same system could upload their resources for the standard. As you might imagine, this was inconsistent at best, and downright useless at worst. My planning time was spent searching the internet for lesson plan ideas. My class periods were spent giving students notes to write down because they didn’t have a textbook they could refer to, so I felt like I needed to give them some kind of reference. Nearly all of my class time was spent lecturing.

The longer I taught, the more convinced I became that my teaching method was horribly outdated and may have actually been harmful to students. Sure, they’re used to the sit-and-take-notes, lecture format of a math class, but given my course failure rates and my abysmal final exam average scores, I knew this wasn’t working. This discontent has led me to research problem-based learning and attempt to implement some aspects of it on my own in my classroom, but these attempts were usually pretty terrible experiences that I don’t really want to re-live.

Last spring, my district formed a textbook selection committee to choose a math curriculum for us to adopt across the district (K-12). They chose two curricula, one for grades K-8 and the other for 9-12. We have implemented CPM (College Preparatory Math) at the high school level. CPM is a collaborative, problem-based curriculum that uses the ideas of mixed, spaced practice for long-term retention. All of these are things that I have read over and over again are best practice for deep student learning that gets retained over time, so I was thrilled to be getting a curriculum that would be in line with all the research that I have done. Continue reading

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The In-N-Out Problem

I did “The In-N-Out Problem with my Algebra Support classes this week. See “The In-N-Out Problem” here.

This conversation introduced our lesson:

Me: “So, have you guys ever been to In-N-Out before?”

5 minutes of discussion, which inevitably includes one kid screaming across the room to another kid, “WHAT?! YOU’VE NEVER BEEN TO IN-N-OUT BEFORE?!”

Me: “Great. Have you ever heard of the ‘secret menu’?”

5 more minutes of discussion, which inevitably includes half the class yelling that they’ve never heard of a secret menu and demanding to know how you can see the secret menu, and the other half of the class still yelling about how much they love In-N-Out.

I introduced the idea of the 3×3, and 4×4, and showed them the picture of the 20×20 (see link above).

5 more minutes of discussion, which inevitably includes someone thinking they are HILARIOUS when they yell out that the picture looks like diabetes.

Me: “No, diabetes is caused by too much sugar. This is heart disease.”

Continue reading

Week In Review – Week 4

Financial Literacy

We started the week with a quiz on bank accounts, balancing a checkbook, and simple interest. After the kids were done with the quiz, I used a pop culture reference to introduce compound interest, which was the next thing on the curriculum calendar.

See, I am awesome. I intersperse my lessons with pop culture references. Continue reading

First Days of School

No, I’m not going to quote that Harry Wong book at you. Actually, my thoughts on that book could constitute a whole other blog post. I’ll restrain myself.

I just finished my plans (by plans I mean flipcharts) for the first week of the school year in both of my classes. Does this seem early to you? Then you must not live in Arizona. We are starting school on August 3 in my district. That is two weeks from Monday. Next week I’m going to Twitter Math Camp, and the week after that is the-week-before-school-starts. I’ll probably be spending 2-3 days down on campus getting all the stuff done that I can’t do at home (photocopying entire forests worth of paper), then we are required to report on the Thursday of that week. Which means Thursday and Friday will be spent listening to our admin talk about stuff, participating in meetings, and wondering why we feel like we’re not ready for school to start on Monday.

This means that I am reporting back to school two weeks from yesterday. Wow.

I’d like to outline what my plans are for this week in each class, partly so that when I can’t remember what I did a year from now, I’ll be able to look here. (Let’s be honest – this is only my 3rd time doing the first week of school. I still have no idea if my plans will work. If someone else wants to use my ideas, go for it. I make no guarantees about the quality of said ideas.)

All right, enough dilly-dallying.  Continue reading

Systems of Equations Introduction

Last year, I was really struggling to teach my Algebra 1 students how to solve a system of equations using substitution. This struggle completely flabbergasted me, because substitution always made so much sense to ME and I found elimination to be harder, while my students LOVED elimination and couldn’t comprehend substitution at all.

“What do you mean, ‘substitute’?” “(Seriously? We’ve been substituting things into equations all year! I can’t even say the word properly anymore because I’ve said it so much!)

“So, I put the other equation here?” (Then they replace the y with the whole equation y=3x so now they have two equal signs.) (Their other favorite thing was to leave the original variable in the equation, so now their new equation says y3x.)

They adored elimination. It was their favorite thing ever. They started adding equations together on problems that didn’t even have a system. Of course, they really struggled to remember to multiply the equation before adding when they didn’t have equal coefficients…but their equation-solving skills were so atrocious that they could somehow still manage to lose the variable they had not actually eliminated…and now I’m just getting frustrated all over again so I’m going to go back to my original point.

Ahem. So I was looking around online last year for a different way to approach teaching substitution as a method for solving systems, and I ran across two ideas, both of which I’m using this year. I’m only going to discuss one of them in this post, because I need to go to bed. I’ll write up my thoughts on the other one later, after I actually implement it next week or the week after. Continue reading

Exploring Graphs of Quadratics

(Link to worksheet file is in the middle of the post. TL;DR summary at the end.)

The textbook we use at our school (Glencoe 2005) has a lot of things that I don’t like about it (why am I teaching the Quadratic Formula before simplifying radicals?) but when I started looking through the chapter on quadratics I found something interesting. After the text introduces graphing a quadratic and identifying the axis of symmetry and vertex, they devoted two pages to this “Graphing Calculator Activity”. The idea was that students would explore families of quadratics by using a graphing calculator to graph the parent graph – y=x^2 – and various manipulations of the graph to see how changing values affected the graph.

I liked this idea, since my students have not had nearly enough time this year to explore graphs and their equations, but I don’t have graphing calculators in my room. Most of my math colleagues have class sets of calculators, but I’m new this year. (This is also the reason my students have not been able to explore equations and their graphs this year.) I haven’t taught them how to use graphing calculators and anytime I’ve needed to graph something in class, I’ve done it on the projector using Desmos.com. I’ve also encouraged them to use Desmos to check their work and even required them to use it to do their homework on Solving a Quadratic by Graphing. (Their graphing-by-hand skills are abysmal.)

A quick comment here: I have about 4 students with their own TI-83 or 84 graphing calculators, including a visually-impaired student whose calculator talks to her. I forgot what a GIANT PAIN IN THE ASS they are to use! Seriously – 2nd > TRACE > scroll down to ZERO or press 2 > scroll across to LEFT BOUND > scroll over to RIGHT BOUND > GUESS > then it gives you the answer Then you have to do it all over again for the second solution?! After spending the whole school year using Desmos (where you just click on the graph and it gives you the coordinates and it doesn’t cost $100), I’m just not doing it anymore.

Where was I? Graphing worksheet. Right.

So instead of using graphing calculators, I booked a day in the computer lab to use Desmos. I created a worksheet that uses all the same concepts from the activity in the textbook, only I edited my instructions a little so my students would understand what I meant. I informed the kids that we would be in the lab, and passed out this worksheet when they got to the lab with basically no explanation. (I probably should have clarified expectations better – see “The Bad” below.) Most of them finished it, and a few finished very early. (Also see below.) I refused to let them turn it in until I was happy with their explanations and observations, which was very good. I made them answer Question #3 the way it was supposed to be answered, and ensured that they were noticing the things they should have been noticing.

Download the Word document (.docx format) here:

Graphing Quadratic Functions Exploration

The Good:

In general, I think my students noticed the effects that different changes to the equation can have on the graph. Their written explanations and observations tended to show a fairly solid understanding of this. Because of our weird schedule that week (standardized testing on different days for different grade levels), I didn’t get a good chance to discuss their findings as a class. I’m also not sure if they truly generalized their observations, or if they retained the information.

My students generally seemed to understand and enjoy the activity. Considering how often my class feels like I’m pulling teeth, I consider this a huge advantage. I will absolutely consider activities like this anytime I introduce graphing in the future.

After spending the whole class period graphing on Desmos, a few kids were fascinated by everything Desmos can do. A couple of students graphed a bunch of quadratic and linear functions on the same coordinate plane and used a variable to animate their graphs. This turned out really cool, and I made them save their work on their accounts. A few kids got to explore all the graphs that Desmos contains in the menu, including crazy polar graphs. Some even noticed the Staff Picks graphs on the Desmos homepage, opened them up, and started playing with them.  This was so awesome – they kept calling me over to show me stuff on Desmos. I’ve never seen them interested in and exploring something that has to do with math before. At all.

The Bad:

I probably should have given my students a better idea of my expectations for the worksheet. I should have explained that I wanted them to make discoveries for themselves; that I hadn’t explicitly taught them the answers to the questions on the worksheet yet. I also should have explained that I was looking for them to use the vocabulary terms they learned in class (parabola and vertex, mainly).

Question #3 wasn’t phrased very well for my students. (In my defense, this is partly because they didn’t read the whole question. They tried to graph y=ax^2 and were confused when Desmos either wouldn’t graph it or immediately defined a=1 and there was no change to the graph from the parent graph.) I should have made it more obvious that I was looking for a general explanation of what happens when you substitute a number in for a.

I didn’t realize how quickly some students would finish, and I should have had an alternate activity prepared for when they did. It didn’t occur to me until my very last period of Algebra 1 that Function Carnival would be a perfect extension for this lesson.

TL;DR

I loved this activity. Almost every student was engaged almost every moment. I have a couple of improvements for next time, most of which were caused by my own inexperience (first-year teacher). I’ll be using similar activities to introduce graphing lessons a lot more next year.