Content of Algebra 2

This topic contains 7 replies, has 3 voices, and was last updated by  mathteacher 7 months ago.

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    Bill McCallum

    This is a repost from a comment in a thread on my latest blog post. It started with the following comment from a user:

    . . . let’s start with the debacle in the appendix that became Algebra 2 and is now part of college and career readiness in my state. The issue simply is: how can one expect to teach that to the typical student in one school year?

    I replied:

    I am always up for a serious and civil discussion about issues in math education K–12. To your question, I agree that forcing everybody to accomplish the standards in 3 years is a bad idea. There are four years in high school, and some students need all four. Many states, districts, and schools struggle to handle that problem in a humane and even-handed way. And because we live in a local-control system, where implementation of the standards is up to each individual state that adopts them (and in some states devolves to districts or even schools), there are many different solutions out there. The standards themselves do not specify an arrangement into courses and do not require that all standards be covered in three years. The near universal agreement that end-of-high-school testing should be required in grade 11, rather than grade 12, has always struck me as strange. That’s not the way it is in other countries, for example Australia, the country I grew up in.

    All that aside, because they were worried that states might want guidance on arranging the standards into courses in high school, Achieve created Appendix A. It was not intended to be taken as a mandate but rather as a model, as is stated clearly on page 2 ( However, understandably I suppose, many policy makers took it as gospel, and that has resulted in the situation you decry here.

    I would point out that the PARCC and Smarter Balanced frameworks did not follow Appendix A to the letter, and put some important limits on the complexity of items for certain standards. However, as I say, I think the real problem here is the assumption that testing happens in grade 11. That should be an option for students who are ready for it, of course, but not the norm. I’ve been saying this for years, but I don’t know of any efforts to change it.

    By the way, if you want to continue this thread, it should probably go over in the forum on arranging the standards into courses. I’ll repost it over there.

    • This topic was modified 8 months, 2 weeks ago by  Bill McCallum.


    I appreciate the response and reposted over here. Those efforts to change what is occurring around the country could come from you and other leaders, especially since graduation, college and career readiness, and many other factors affecting kids are in play. The common core standards put this issue in motion, and, although some of the consequences may have unintended, they are still the responsibility of those who set this course in motion, especially that ESSA, PARCC, and high-stakes testing are in play.

    As far as PARCC goes, I would disagree that they put limits on the tested standards. In fact, didn’t PARCC “invent” standards to be tested? These are some of the integrated, C, and D standards. One standard even asks high school students to “use reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity.” PARCC has interpreted this to mean that students can use right triangle trig on non-right angles, for example. PARCC has revised and re-revised the PLDs several times. Algebra 1 students are also tested on “securely held knowledge.” The common core standards put this chain of issues in motion.

    And, from my experience, asking elementary students to take a high stakes test that takes 4 hours is a bit much. The high school test is 4.5 hours long. Way too much testing. The common core standards put this chain of issues in motion.

    Finally, I do appreciate an honest and candid dialogue. Many of my colleagues and I have been frustrated as we find the balance between content and mastery, especially in Algebra 2. We have seen high failure rates on PARCC, as defined by 3 or lower, and then told that high failure rates mean that PARCC and the standards are so rigorous. So rigorous as to be unattainable. We have even been told that unless a student is in the 60th percentile in math (on MAP tests, for example), they cannot get a 4 or higher on PARCC. We are frustrated because it is not possible for all students to be greater than the median. The common core standards put this in motion.

    We are champions for our students and want them to succeed. We have high standards for ourselves and our students. We hope that those who set this in motion can see what has transpired and help us in the efforts to truly help every child succeed in math.


    Bill McCallum

    Thanks for the reply. A few thoughts in response.
    First, I haven’t kept track of all the PARCC changes and I think you are probably more up on them than I am, so I take your point there.

    On testing I have mixed feelings. I get the frustration people feel about too much testing and I think it would be a healthy move to reduce the amount of testing (and that seems to be happening). I don’t think it is a healthy move to opt out altogether. So there has to be some balance in between (something this country is having trouble achieving in all sorts of areas). What I don’t know is where that balance point lies. Partly it will be determined by political forces, of course, but is their empirical evidence to help decide? You say 4.5 hours is too long for a high school test. As someone who grew up in a country where the high school test was 3 hours long, I’m inclined to agree. But how do we come up with these numbers? Do we just take the average of everybody’s gut feelings? I wish we had a more empirical approach.

    Finally, on the question of responsibility: well, I have pretty much devoted my life since the standards were written to helping teachers understand and implement them and advising curriculum writers, assessment writers, and policy makers on what I think is their proper use (spoiler: standards are not curriculum and standard are not assessment frameworks). I can’t control the extent to which my voice is heard. Illustrative Mathematics, the non-profit I went on leave from my university position to found, has just completed writing a complete, freely available, grades 6–8 curriculum, and are hoping to continue on to high school. Stay tuned!



    I do appreciate the response, but honestly, I haven’t seen evidence of advocacy for students from any of the authors of the standards. As evidence, you champion your completion of a middle school curriculum, which is not available today but will be available this summer, a full 7 years after the standards and a full 6 years after the adoption by my state. With all due respect, it is like the teacher who reviews before a test solely to tell parents that they reviewed without any thought about the students who will take the test.

    This middle school math curriculum is at least 6 years too late and honestly, if it took the authors of the core standards 7 years to write a curriculum for grades 6-8, what chance did the locals have? I should point out that we received nothing in terms of curriculum from our state and created everything ourselves locally with little funding. I must admit that I am shocked it took the people who wrote the standards 6 years to figure out a scope, sequence, and curriculum. We were only given 6 weeks.

    As I mentioned, I’m not sure about the level of advocacy on your end. But what I saw during the last presidential administration was that they shoved the standards at states by requiring them to adopt and take money (RTTT) without understanding that No Child Left behind was still in effect. That is, we had 2 sets of rules to follow, often contradicting sets of rules. Only last year did the previous presidential administration reauthorize NCLB as ESSA. This has left long lasting issues and major problems for locals, including the lack of primary resources for classroom teachers.

    The larger question is what leaders such as yourself, can do now, especially as states try to comply with ESSA. I would encourage you to work with local states, such as Maryland. I would encourage you to look at specifics to see exactly what has happened. For example, look at the PowerPoint regarding ESSA presented to the Maryland state board of education (in the May 2017 agenda) and you will see how your message (“standards are not curriculum and standards are not assessment frameworks”) has not been received by states. Maryland’s entire plan is about “compliance” and is not about learning nor about students. As I have mentioned, this is an unintended consequence of the rollout and structure of the standards.

    Perhaps I will see you at NCTM in the fall and we can talk more specifics.


    Bill McCallum

    If you want to talk at NCTM you will have to let me know who you are.

    • This reply was modified 8 months, 1 week ago by  Bill McCallum.


    Hello Math Teacher, As a MO HS math teacher, I definitely feel your pain. MO “voted out” CCSS in 2015. When our rewriting committees got together, they found out what a huge project rewriting is. When they started comparing with old MA standards, old MO and others, I’m thinking they figured out the CCSS writers did a lot better job than they realized because they kept most of CCSS, mostly just tweaking wording…except for Algebra 2. MO Algebra 2 is really bad now. I have gotten involved by volunteering on committees, doing a lot of listening and reading to understand from multiple perspectives. It has eased my frustration to find no one who is intentionally messing up students here in MO.

    I agree with you that with unlimited talent and funding, the implementation could have been a lot smoother. It was unfortunate how much time, money, and talent was diverted to politics. I might be wrong, but it seems like the more the CCSS writers and supporters try to help from the top, the more people who do not understand the whole picture feel like CCSS are “top down.” So what I’m trying to say is that I think it’s best to work for change on a state level. I’m seeing some cool progress and you seem to have the passion it takes to make a serious difference in MD as well.

    You mentioned not being able to cover all the Alg 2 topics. One tool I’m leveraging is a list of topics commonly found in Algebra that should not be there. It’s linked in the third paragraph from the bottom this article: I use this list to help wherever I can to keep the Algebra 2 content manageable.

    Here’s another piece where you can see my journey to figure out why Algebra 2 is such a mess:


    Bill McCallum

    Thanks Lane, I love your list, and agree about the need to prune topics carefully.



    I realize that it is summer, but it has been a month since we first started this thread and students will be returning to school shortly. Has there been any political movement on your part to help locals with the burdensome rules set in motion by the common core with respect to college and career readiness, graduation requirements, ESSA, the demise of PARCC, and so on. As I have maintained, these may have been unintended consequences of the core but nonetheless are the responsibility of those who set these into motion. Many of my colleagues and I have been active both locally and nationally but we have yet to see any leader of the movement speak.

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