A few nights ago I was working on an assessment and I spat this in my twitter machine:

I do this often as a way of talking to myself while working on things late in the evening. Often it's just to be funny, sometimes it's a little more serious, but I always I figure it's late and not a lot of people are reading. Not so much this time. It happens. There were a few reactions I want to address though, as my use of "points" there was misinterpreted in a couple ways.

Don't use them!

Ideally, yes. I feel you here. Unfortunately I have a gradebook I have to maintain with a minimum number of assignments per grading period, so I've got to do something.

Let the kids decide!

I tried this once before. In 2015 I implemented A/B/Not Yet grading in Calculus. We'd take an assessment, kids would look at the solution, and then rate themselves. Generally, kids were not adept at rating themselves. I had no good system for dealing with students who rated Not Yet, I was too busy with athletics to have any kind of viable after school system. Collecting the ratings was very time consuming and I was poor at communicating how to determine what should be what. A rubric you say? At that point this work saving system has now become more work than another system would be, so no thanks.

It was interesting experiment, but one I chose not to continue. Your experience may be different.

SBG!

I never never never assume someone is familiar with my teaching journey. These responses were expected (and welcome!) and I chose not to reply to them, because it'd be too easy to come across as that guy who is all "well I wrote the book on SBG blah blah blah..." because that's not a good look. But to those who suggested SBG, yes, I love it as a system and it works super great in a lot of contexts. I have used in Algebra 2, Pre-Cal, and College Algebra with great success. If you are interested in my history with the systems, I believe I have tagged the posts appropriately.

What I do these days...

In general, most classes work great for SBG. I have an SBG system in place with College Algebra and the kids like it. It's extremely similar to the system I came up with a long time ago. However, AP Calc has really never been SBG friendly in my opinion. Implementing a built-in retry system is really the problem. And with the speed you have to move with AP Calc, eventually in class assessments just become a burden. Last spring, AB Calc shifted entirely to free response based assessment because that's what we needed to do. It didn't work, but I still liked it and have some thoughts for this year. In general, with Calculus I will break stuff into a topic, assign some general value to the category, and give a handful of questions about that standard. The points vary, the kinds of questions vary, and there is no built-in retry. It's not really SBG. It's also not a test worth 100 points.

Here's the assessment I was working on when I tweeted:

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This particular assignment was for my BC group. The complaint was about how to weight the various sections based on the time it would take to complete them and the complexity. When I grade something like this I take an overall picture of the work. I check for correctness, offer comments, and give students a chance to discuss their work with others. Each one of these sections is an entry in the gradebook. But 1 point ≠ 1 correct problem, I take the whole body of work into account based on any trends in error I may see.

Maybe that clears things up, but maybe it doesn't. Non-traditional graders of the world I'm very with you.

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AuthorJonathan Claydon

Last week at NCTM 2018, I presented some thoughts from a radical Algebra II experiment I ran some years ago. While Algebra II was the center piece, the topic is broader. What story are you trying to tell with your curriculum? How do you integrate pieces so that students can see a theme in the skills and concepts they learn throughout the year? Why should what you teach in September matter in April?

This is a summary of those ideas from my talk.

The Script

The textbook models of Algebra II are pretty consistent. A whole parade of function types, done in isolation, over the course of a school year. Your experience probably looks something like this:

I dutifully followed a script similar to this for four years of Algebra II. But there were lingering problems. In the Fall of 2012, I included this as part of my final exam:

I made what I thought was a fair assumption: we had covered linear, linear systems, absolute value, and radical functions throughout the fall system and students should be able to work with them when mixed to together.

I was completely wrong. Students had forgotten fundamental algebra mechanics and were thrown trying to remember not only how the non-linear ones were dealt with differently, but even what they were in the first place. The topics we discussed had been so spaced out that students had made no valid connection that equation solving is a universal thought, different functions merely introduce new mechanics.

Second, we had this section in the book on parent functions. There was an activity that accompanied it:

Students spent a class period matching equations, words, and graphs together to form a parent function library of sorts. Then we never talked about this activity again. It served no purpose other than to say "ooh, activity!"

The Flip

I spent the summer of 2013 frustrated with Algebra II and determined to find a better way. There was good material in this course, but it was being handled in such an awful way. The messaging was all wrong. If you take the Texas State Standards for Algebra II and make a word cloud, you get something like this:

Clearly, the individual functions themselves are not the most important players here. Equations and Inequalities are the most frequently used terms. Incidentally, you see how small "real world" is there? Probably could stand to fix that too.

I revisited the parent function activity and thought: what if this was the entire course? What if we talked about parent functions at the very beginning of school and referenced it throughout the year? What if we focused on not just solving equations with one function at a time, but with many functions at time?

Pivot Algebra Two was born. Let's have students see how a set of skills play out with many different kinds of functions all at once. I divided the curriculum into two parts. Part 1: linear, radical, quadratic, and absolute value. Part 2: log, exponential, rational, polynomial. In each part, we would do overviews of the skills in play and slowly spiral up the difficulty.

In addition to taking tons of times to play with equation mechanics (roughly 6 weeks on linear, quadratic, absolute value, and root functions with increasingly higher difficulty), students got to see connections between their work and graphs. I don't know about you, but prior to this experiment, my kids hated graphing. It was a tedious process that seemed unrelated to anything. In this vision of Algebra II, I was going to give graphs a purpose.

The Motivation

When it was time to start a month of graphing, they groaned. As the ones that came before, they hated graphing and didn't understand the point. But then I took some classwork we had done previously. At this point they all agreed that solving equations was super easy. I graphed one side of the equation, and then graphed the other. I clicked the intersection points. MINDS BLOWN. The graph and the equations are related! I can check my answer easily! I don't need your help anymore!

It was a beautiful moment. I used it as a jumping off point to more complex algebra. In both our look at advanced quadratics and logarithms, we started with the graphs. We know that the intersection point of two graphs is equivalent to the solution of the equation. What algebra do we need to prove that?

Kids saw the power of the quadratic formula. They saw transformations for what they were, ways of manipulating various parent functions into equations.

Then we summarized what we learned about our first four functions:

The Payoff

The efficiencies in this system were apparent pretty quickly. I was no longer reteaching simple algebra moves. Kids had them down. We could tackle mechanics previously unheard of in Algebra II. We even put logarithm properties to good use with problems like this:

There is a lot of overhead in this problem. You have to understand how logarithms combine, how they are undone, that the resulting quadratic has two solutions, and that it's possible not all of those solutions are valid. And, to my sheer astonishment, the kids were telling me this was easy. Absolutely bonkers to think that this problem, which take a good 5-6 minutes of kid time to work, was easy! I'd ask if they need any help and they'd say, nope, I can just graph it.

These connections also help improve their ideas of equivalence. We could take any line in this process, graph it, and see that the intersection points had the same x-value. We were manipulating a log into an equivalent parabola.

The Longterm Lesson

This line of thinking, finding the story in my curriculum, continues to pay off. Because of this exercise, I have improved my ability to weave concepts together in other courses. I no longer teach Algebra II, now I'm primarily focused on Calculus, but the fundamental thought behind this experiment remains. Calculus has a story, and students should be able to see it.

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Calculus is even better suited to these ideas. Limits, Derivatives, and Integrals interplay with each other in all kinds of ways. What if students saw that relationship from the very beginning of the course? What if they didn't have to wait 4 months before they even heard the word "integral?" How much better could they be at seeing those relationships?

The Conclusion

I encourage you to take a hard look at what you teach. What are the big ideas? What should students be able to do when it's all over? How can you give them an overview of their year in the first month of school?

For more detailed information, I chronicled everything about my radical journey through Algebra II. Please contact me if you need anything.

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AuthorJonathan Claydon

A series of seven posts on major turning points in my teaching career. A study of where I was, where I am, and where I'm headed.

ALL POSTS IN THIS SERIES

Curriculum has fast become my favorite focus in recent years. It started with an observation as I taught Algebra II, that the way I did things was inefficient, uninteresting, and lacked depth. Students were doing surface level material and never getting very far in a particular topic. There was a lack of cohesion in the school year. It felt that we were just studying things at random, hopping around on a whim. I want curriculum that's interesting to teach and that spends 9 months telling a story with identifiable payoffs.

This is different from a discussion of individual lessons. I'm talking about big picture. How do you create the tool that drives the school year?

Where It Was

I followed the textbook, roughly in order. My first year I spent a lot of time relearning the material, just trying to make sure I didn't make any major mistakes the next day. Even then I still screwed up, a natural process when teaching something for the first time. I wasn't worried about what message I was trying to send over 9 months, I was just worried about making in through to the next Friday. As I was transitioning into standards based grading, I noticed that the curriculum just wasn't satisfying. Planning this way is also just terrible. I have sat in on one two many conversations that go "well, we have 2 days for 1.1, and 1 day for 1.2, but we HAVE to finish 1.3 by Tuesday..." Ugh. Just, ugh. What generally happens 9 months later when you plan like this usually includes the phrase "...we just ran out of time." This shows a lack of vision. In August, you should have some idea of where you want to be in May, with a working knowledge of how to get there.

The week to week stuff just stopped cutting it for me.

At the same time, I also realized that students do NOT care what chapter you're in, or what the section number is, or any of that textbook organization type stuff. They are, however, slightly more interested when you talk in topic names.

The use of SBG and topic names had an effect on the way I discussed curriculum. I stopped caring about chapter numbers and section numbers and instead focused on the material itself. It wasn't Chapter 5, Section 2 anymore, it was Motivating the Quadratic Formula. That was an important step I think. When you view a course as a collection of topics, you're more inclined to organize them into something that makes better sense to the student.

Algebra II, a course I will always defend, offers a great case study. Is it necessary to deal with the start up cost of solving equations 5 disparate times through the school year? Could you cover all the mechanics up front?

Where It Is

It was those Algebra II questions that lead me to a very intense project, my Pivot Algebra Two idea from 2013. Rather than think about the course as a list of functions where you work on the same skills weeks apart, what if you focused on the skills and iterated through their applications for various function types?

This skeleton lead me to rewrite the entirety of Algebra II around the major skills I wanted students to develop. I wanted the basic operations we learned in August to help us with more challenging situations in May. Along the way we could take a minute to summarize what we had applied to a subset of functions.

The end result was the most fun I've had teaching. We went really deep into topics that were unthinkable before. We had time for awesome projects. It was a great group of kids. All of it driven by a cohesive narrative. The project paid great dividends down the road.

My initial run at Calculus was challenging. I spent the following summer grinding away at the curriculum, looking for inefficiencies. I was searching for my narrative. After a lot of work I found it: the integral and the derivative need each other, let's explore the many contexts of their relationship. The result was a road map that gives students a basic idea of the course in about 5 weeks.

No saving things until later because they "weren't ready" or something. The more a student knows about a course up front, the more you can with the material later, the more you can communicate the story of Pre-Cal, or Geometry, or whatever.

Where It Is Going

Thinking about the story I want to tell with a course has been a huge breakthrough. Textbooks are of little concern to me. I use them as reference to get an idea of a course's topics and building a model document from there. For example, next year I will be teaching Calculus BC for the first time. I will consult a textbook but the actual rhythm of the course will find its way into some document like the one I use for AB. There's a possibility I'll be doing College Algebra as well, meaning a return to the idea I started in Algebra II. As an instructor, manipulating curriculum in this way has made me incredibly familiar with a course. I could write pages and pages about a logical progression of Pre-Cal from memory. I've been thinking about the interconnection of its topics for years.

Every year I find it easier and easier to fine tune a curriculum. Delete some wasted days here, find a new connection here, and carve out room to go deeper.

One of these days I'll figure out a way to take these personal notes and develop them into real guides for people who want to do the same thing. It's been several years, but that was the concluding step for my Algebra II project.

Takeaway

Many of you are probably in the same position. I know lots of teachers who have little regard for the order preferred by a textbook publisher.

When you sit down this summer to think about your courses, consider the story you want to tell. What connections do you want to establish? How can you spiral back to information as much as possible? How do you want August to influence May?

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AuthorJonathan Claydon

Since my Algebra II experiment years ago, I've been obsessed with students to start making connections between graphs and algebra. Fairly consistently I have students who dismiss graphing and something uninteresting because no one seems to making connections about why it's so interesting. That's it's possible the "x= " they're able to find with a calculator represents something. Pre-Cal has some algebra objectives and I've brought what I learned with that experiment along for the ride.

In addition to emphasizing graphing, I've been demanding a lot of explanations from my kids this year. A go to for a while now has been justifying a situation. Recently I gave kids a graph and three possibilities. In class we focused on the quadratic formula, it's super solving powers, and it's ability to show you the x-values of the intersection points for a pair of functions. In the setup for this question, I didn't specifically ask them to use this method, though most went with that approach. Here's a representative sample:

The brute force method. The student solved all three and made a connection to the picture with their work. Nothing wrong with it.

However, some found other ways:

An excellent observation of graph transformations. The functions used were simple enough that spotting some features was a quick way to accomplish the task.

The next student made a similar find:

Not only did they attempt a quadratic formula solution (apparently done on the calculator and not recorded) but they weren't satisfied that the mere presence of an imaginary number would do the trick. The slope of the line was important!

This last one might be my favorite:

Not only do they grind through the quadratic formula here, but they remember that if those intersection points are solutions, they are useful! I think only one other student (out of ~60) tried this out.

I was pleasantly surprised because I only had one method in mind when designing the question, forgetting that kids could wander in so many interesting directions.

Posted
AuthorJonathan Claydon

Curriculum is a current focus of mine. In recent years, I worked through thought experiments on Algebra II and Calculus curriculum. What happens if you ignore a textbook publisher? What if you start with the standards and find a spiraling pattern that makes sense? Can you find the themes? How will what you teach in September help your students in May?

Viewing your course in broad strokes has proven to be very valuable. In Algebra II I only got one year to play with it, unfortunately there was no follow up. Calculus is very much a continuing experiment. Upon taking over in 2014, I knew it was a five year project minimum. Deploying a curriculum of my own design was going to be a really big piece.

With another round of AP scores to analyze, what needs to change in that vision?

More pressing, what has crafting a vision for Calculus taught me about Pre-Calculus?

Pre-Calculus has some themes: raw algebra, trig, polynomials, and a random bin of parts. Can we tie those together better?

At TMC 16, on Sunday July 17, I'm going to offer an opportunity to participate in this thought exercise. Does the curriculum we work through have to be something we actively teach? Do the standards have to match the one from our state? I don't think so.

I've worked through 8th grades standards and Algebra I standards before, neither are things I've ever taught. If you want to broaden your horizon of how math concepts go together, I think it's well worth the trouble to read about all the things you don't teach.

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AuthorJonathan Claydon

I missed most of the fireworks, but apparently Algebra 2 was on a lot of minds the other day.

I'm going to +1, or Like, or Heart or whatever this statement. The course designated Algebra 2 manufactured by your average textbook is the worst thing in the world. It could be really interesting, but it's foundations are fake. The problem is, everyone is scared to tell the kids it's all fake.

The Texas Standards defining Algebra 2 are five pages (Algebra 1 is five, Geometry and Pre-Cal are six for comparison), and use the phrase "real-world" three times and the word "life" three times. It's really just a list of a random assortment of things. No suggestions on just how you might want to wrap what you're trying to sell. Naturally, your textbook/teacher just fakes it. "Oh, well it's important to know the real and imaginary roots of a 4th degree polynomial because......" or "Logarithms are excellent models for...."

Just stop it.

When I taught Algebra 2 traditionally I got exactly what I deserved, kids remembered 30% of a random list of things and saw very few connections between them. The topics sat in their silos as we kept checking the boxes on the list. And I sat in meetings wondering when the kids would ever get it.

There's a tangent argument about that view and the design of college math placement exams, but maybe another time.

Ok, Algebra 2 sucks. Thanks for sharing, you say.

I'm not sure how I can raise my hand more enthusiastically or force my pro Alg 2 thoughts into the timeline (I spent like, all of 2013-14 talking about it). I embarked on a really crazy experiment a few years ago and the results were eye opening. The work remains unfinished, but it was an important foundation. If you cut the bullshit, there are some interesting things in this course. But locally, I couldn't get anyone to listen to me. Because the textbooks didn't agree with me. And following a textbook is easier.

But I wouldn't change my approach. My students responded because I was honest about what I was trying to teach them. I stated a specific goal. We're going to do a lot of impractical things here. I'm not going to lie to you about their uses. It was going to be a math class for the sake of learning math. This is going to be an experience in Math Language, not Literature. And we're skipping all the big time nonsense (shout out to complex conjugates and 4th degree polynomial solutions!). Algebraic manipulation, while not particularly real world, can be interesting to a seemingly uninterested population. It's not an insane proposition.

At the end of the year, when we spent a LOT of time talking math sentence structure and grammar, I opened up our discussions. I showed them modeling and authentic scenarios. We had the kind of big idea conversations you want in a math course.

Most of their course work was fake work in a fake world. It was variable and coefficient manipulation. Over and over. It was verifying algebra with graphs. Over and over. But I can tell you this intrepid group was with me the whole way. Disinterested is not a word I would use to describe them at all. They enjoyed being good at Algebra because I wasn't trying to fake the purpose of Algebra (nor did I overload them, a lot of material was cut).

Conclusion

In my opinion, the goal of Algebra 2 is to expand a student's vocabulary (insert "toolbox" or other cute ed-metaphor here) of mathematical functions. It's a lot of fake stuff that regular people (and even me outside of teaching contexts) never use. Much of the content needs to go. The entire focus of what the content is needs to change (widely applicable processes vs function family checklist). But more students could be taught to appreciate the underlying ideas, as long as we're stuck with it.

I don't know, I'm at a loss at what else to say. The amalgamation that is Algebra 2 can be saved, it can be done in interesting ways, real live (not just the math weirdo) random kids can be taught to appreciate the beauty of what's going on. You just have to be honest.

To the broader argument of Algebra 2 being some sort of necessary force to getting kids into college? That's junk. And I agree with Dan on the misguided power we've given the course. This is a problem that starts at the top. College Algebra and Math Placement Exams are fake products and students who are successful in them have fake knowledge. Until you admit that's the problem, you're going to keep staring blankly at the wall wondering why 19 year olds who just want study political science hate rational expressions.

I'd love to know if I've missed something in this whole kerfuffle.

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AuthorJonathan Claydon
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Last year I rattled through some frequently asked questions.

People point to me as a user of interactive notebooks. I would not call my notebooks interactive in the same category as what the internet considers an interactive notebook. If you're looking for foldables, tables of contents, and scripted notebook pages, please go check out Sarah Hagan. She even had a whole day celebrating her.

Anyway, this is what I do to get students to do stuff. Time for bullet points!

Gallery

Here's some pictures. I'll do a little explaining after.

Structure

  • composition books preferred, hold up better over time
  • students can keep them in the room, I use a 30 qt. tub for each class
  • colored duct tape identifies the class period
  • a manilla folder fragment stapled to the back holds old tests
  • students track their SBG scores in the front, it's not a table of contents

Procedures

  • students use it every day, no questions
  • all classwork and notes are contained in the book
  • from time to time work is pre-typed and handed out on 1/3 or 1/2 sheets
  • students do a lot of work copied from the board
  • students don't have homework, they work when they are in class
  • students can use their books on tests, tests are designed to be about thinking, not parroting, we don't do review days
  • class time is intended to provide as much student time as possible, stop talking
  • books are checked every 3 weeks for updated SBG charts and cleanliness
  • students can put things wherever they want
  • assignments are graded a day or so after completion, I walk around with a clipboard while students are working on something newer
  • it takes time to cut things out and glue, I mean, just accept it
  • I never take them home
  • kids forget them, it happens, usually not a chronic issue

Critics of the notebook thing dislike the time required for the cutting, taping, gluing, and preparation. They'd prefer a binder full of daily worksheets or something. Mine don't suffer those issues. I don't find myself spending an inordinate amount of time waiting on kids to do stuff. Of course, I've set up class to be for them. You don't see me talking much. Assignments are short and sweet so they can do all the cutting and still accomplish something. I'm allergic to full page handouts. Over time it's just so much paper. That volume of copying is just unnecessary to me. Same with packets. Yuck. One year I'm going to count how little I copy as proof.

After five years with these things I'd never do binders or folders, ever. Student productivity is at ridiculous levels since I made it a requirement.

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AuthorJonathan Claydon
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Frank had a few thoughts to consider a couple weeks ago.

I got to thinking, do I overtest? Would the tests I give be considered high stakes? Having implemented a standards based system for several years, I have tons of data on the idea. I think the answer to the first question is "maybe" and the second is "no." Though I think my students disagree.

Raw Numbers

Some notes: SBG was introduced in Algebra II as a mid-year experiment; in 2011 and 2012 I gave a one time test of basic skills at the beginning of the year in Pre Cal before the SBG style tests began. In 2012 I gave fewer Pre Cal tests because, ironically, Texas toyed with the notion of increased standardized testing: 15 exams required to graduate high school. We administered benchmarks and real versions of all those tests that school year, in addition to the previous slate of tests still required for the class of 2013. That summer they retracted the plan after public outcry.

I allow about 40 minutes for each test. They happen every 7-10 calendar days. What I think is missing from Frank's numbers is a considering of that old stand by the quiz. Usually at least two quizzes accompany those three term tests, and take about 20 minutes each. Also, it is more common for schools here to have six terms per year. Estimate 15 tests and 12 quizzes per school year and you get about 14 hours, excluding the final.

My Opinion vs Student Opinion

If you ask my students, a lot of them would tell you we test a lot. In the case of testing successive Fridays, that's when many will moan "didn't we just have one?" If you ask the right followup questions, you can get them to see beyond the gut reaction. Do we have quizzes? No. Do you have more grades? Yes. Do you know more about how you're doing? Yes. Do you have homework on top of all of this? No.

I have had them interviewed before, year after year, lots of feel like they have a more specific idea about how they're doing. They can misfire on one part of an assessment but celebrate success on another and come out feeling like they learned. They can share heartbreak over coming oh so close to that elusive 4.

The Stakes

Are these test high stakes? I don't think so. My students get nervous about them, sure. They THINK it's life or death (thanks grade culture). Some of them really push themselves to get double 4s as much as possible. A lot are ready to have a shot at improving something that didn't go well previously. How do I know they aren't high stakes? I have watched the data for years. The standard 15 unit tests allows 15 attempts at 15 test grades. My students have over 80 attempts at 40 test grades. One misunderstood topic in the mix doesn't make a dent.

At the end of some grading terms, topic 7 or 8 might make a 1 point difference. Nobody fails a grading term for an isolated problem, it takes a series of miscues. At I've noticed the problem long before it's ever actually a problem.

I think a better question is: what are you getting from your 14 hours?

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AuthorJonathan Claydon
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Help me out here, Algebra II people, we have a problem.

The answer I'm looking for, is "where does the given parabola intersect the line y = 7?"

One of the first things I decided to cover in Pre-Cal this year was solving quadratic equations. It creeps up on you in Calculus and beyond that I don't want my students to wait until they're 22 to realize its value like I did.

When I introduced the topic, I asked "why do quadratics have two solutions?" In every class someone suggested it had something to do with the x-axis. I pushed and wondered "what's your obsession with the x-axis?"

I tried to confront this problem last year with my method for introducing the quadratic formula. Students saw the quadratic formula only as a means for finding x-intercepts. They are not totally wrong, but they don't know the truth.

Part of this is the fault of textbooks. As I noticed last year, there is an obsession with giving students quadratics that are equal to 0 and equating roots, solutions, and zeros as like terms. When really, what they need to understand, is you can construct a quadratic which in turn has x-intercepts that are equivalent to the intersection (or lack thereof) of the starting expressions.

Compounding the problem is then showing them half a dozen methods for solving, muddying the waters the whole way. Should I factor? Should I complete the square? What about this formula thing? Students have no idea where to start. Every class admitted this to me. All of them could tease out factoring and the quadratic formula as methods, but very few could describe when one is more desirable.

I'd love to admit that my returning Pivot students nailed this question like they should have, but that wasn't true.

The traditional treatment of quadratics and what the two solutions represent does more harm than you think.

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AuthorJonathan Claydon
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A year ago I embarked on a wild idea. Algebra II as a subject is taught in a broken way. The goals of the project:

  • Students can recognize an equation of any function type at a glance
  • Students are comfortable manipulating parent functions of any type
  • Students aren't scared of decimals or 10-step solutions
  • Students can connect algebra manipulation with a graph
  • Students don't think there's anything special about an inequality

I wrote a plan and spent a school year making it up as I went along. What's practice look like? What do the assessments look like? How extensive will we study rationals?

It was an experiment in every aspect. I never knew what was going to happen more than a day or two in advance. As if changing the entire curriculum wasn't enough, I tasked these students with two ambitious projects. That I made up randomly.

Estimation Wall? Improv. Algebra Wall? Improv.

All I can say is that the experiment was a complete success. The kind of algebra these students were doing at the end of the year was unthinkable a couple years ago in an academic-level class. In certain aspects we were beyond a PreAP level.

And now you can try it yourself!

My Algebra II resources have been very popular this year. If you've found your local Algebra II resources lacking, mine have been freshly updated with everything you need to approach Algebra II in this excellent way.

SBG Assessments? Check. Practice? Check. Activity Ideas? Check. Final Exams? A formalized outline of the curriculum you can use to start a meeting with your Algebra II team? Check.

Before you get too excited, there are some shortcomings. I did not meet all of my goals. You should know in advance that:

  • I could've done a better job with inequalities, students were ok with the mechanic but I have this nagging feeling they never conceptually understood x = 3 vs x > 3
  • I never got to conic sections, like, at all
  • I don't like the names I used for my assessment standards, students were confused and the SBG system was kind of compromised as a result
  • I covered systems of equations without ever calling them systems of equations
  • I never stressed simplifying radicals, I had them fiddle with decimals instead
  • I barely talked about factoring, my students even rejected it in favor of the quadratic formula, and I never touched it when dealing with rationals
  • I could've included more material to enforce domain and range, I introduced it and tried to reinforce when discussing the boundaries of solution regions, but many students found it to be a struggle, and I have no idea why
  • I didn't stress complex solutions a lot, and I never got into the mechanics of complex numbers
  • I didn't discuss rationalizing denominators or complex conjugates
  • I only scratched the surface of polynomials, it was relegated to a vocabulary unit

That means there's room for improvement. Due to the needs of my department, I won't be teaching Algebra II in the future. But, the experiment gave me a much better understanding about how the topics of algebra connect. As a result, the lessons learned here will have an impact on how I teach Pre-Cal and Calculus.

On the off chance you're going to TMC14, the results of this experiment will be discussed in the Algebra II morning sessions.

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AuthorJonathan Claydon