Posted on

eMath September 2017 Newsletter

A new school year has started in the great Northeast. The light is getting dimmer while the trees are getting prettier. We’ve been all sorts of busy this past month at eMathInstruction working on making our site easier to use and coming up with add-ons to the courses. Let’s get right into those.

Let’s begin with the Common Core Algebra I Add-Ons. This month we’ve added two new lessons. One fits into Unit #3 between Lesson 6 and 7 (so I’ve given it Lesson 6.5). The lesson title is Motion and Average Rate of Change. We’ve seen quite a few motion problems on the Common Core Algebra I Regents Exam, so I thought it was time we devoted a lesson just to them. We also added Unit 4 – Lesson 9.5 on Solving Absolute Value Equations. We emphasized simple algebraic equations and more complicated graphical ones. Interestingly enough, there is no mention of solving any absolute value equations algebraically in the Common Core Standards, only graphically. Which is why you’ve only seen them that way on the Regents exams. Here’s a good example from June of 2016.

Moving right along to Common Core Geometry, recall that our add-ons to the Common Core Geometry curriculum this year will be the Unit Reviews and Unit Assessments. This month we’ve added on every student’s favorite, Unit #3 – Triangle Congruence Proof. We’ve given you a long set of additional problems and a nice assessment. We’ve also published the standards alignment documents in our Table of Contents section. If you’ve been itching to do some standards mapping to our Geometry curriculum, check out that link.

For our Common Core Algebra II Add-Ons this month we bring you an additional assessment and lesson. We created a Unit 3 Formative Assessment make up exam. This rounds out the Form B exams for Common Core Algebra II. Now each unit has both an assessment and a mirror make up assessment. We may consider adding additional make up assessments if teachers think it’s a good idea. We also added a lesson to Unit 4. Lesson 7.5 is titled Exponential Modeling Revisited and looks at moving between time units in exponential modeling. For example, if a growth model is given in hours, what would its equivalent look like if modeled in days instead. We’ve seen numerous questions on the New York State CC Alg II Regents exam on these types of questions.

Finally there is the old-faithful Algebra 2 with Trigonometry Add-On for this month. After a great deal of resistance on the part of yours truly, I’ve finally created a lesson on factoring trinomials with a method other than guess and check. I created Unit 3 – Lesson 6.6 – Factoring Trinomials Using the AC Method. Teachers who are familiar with this method of factoring already probably have a sense for how this lesson will work. I still believe guessing and checking is important for students, but this method does work and does produce reliable results, at least it does if a student can find the two integers that satisfy the product and sum conditions.

A final note on add-ons in general. I’ve been struggling with how to arrange them and have decided to keep placing resources into the add-ons so that they are in Unit order. That means add-ons from last year mix with ones from this year. For teachers who want to only see new add-ons, this isn’t the greatest way of organizing them. Still, for the teacher who just wants to see what resources are there for a particular unit, this is a very effective way to  have them arranged. As always, if you have any thoughts either way, feel free to reach out to me.

In other New York Math News, it looks like the Board of Regents finally voted on and adopted the New York State Next Generation Mathematics Learning Standards (or NYSNGMLS). Click on that link to open the full 170 page pdf document on the standards. They were just adopted so there are many news articles on them. Here’s a good one out of Albany itself:

Goodbye Common Core: New York’s New English, Math Standards Are Here – Albany Times Union

One of the most important parts of this piece is the following excerpt:

I’ve been waiting on some official word of the timeline before we started to modify our own text. Looks like I have a few years to make that happen. We may, when the time comes (2020), publish a New York edition to our Common Core texts. I’m hopeful by that time we’ve moved to an electronic only textbook. Thanks to Brian Battistoni, my good friend and colleague from Arlington High School, for the heads-up that the Next Gen standards had been officially adopted.

Well, I think that’s it for now. I’m hopeful that everyone has had a good start to their school year. As always, if you are having any troubles with your subscriptions or any suggestions on the curriculum, don’t hesitate to email me at: I’m busy, but never too busy to help.


Posted on

Common Core Algebra I Scale Maintenance and Lake Wobegon Syndrome

So, the Common Core Algebra I exam was given this morning and the conversion curve was released as well. We had received advanced warning, about a week ago, that the state had done some “Scale Maintenance” on the Common Core Algebra I conversion scale. The memo was, as usual, filled with technical jargon out of NYSED, but one line caught everyone’s attention (all five of us that read it). The line went something like this:

With the curve maintenance, we expect more students to pass the Common Core Algebra I exam and more students to achieve higher grades.

Now, why would the curve need maintenance? Well, when the Common Core Algebra I exam was first given in June of 2014 a curious thing occurred. NYSED decided that they would make the percent needed to pass the test (scaled to a 65) pretty much the same as it had been on the Integrated Algebra exam. This raw percent was right around 35% of the test points earned. So, they made the test still relatively “easy” to pass.

But, the seismic change that happened to the conversion curve was the score a student needed to earn an 80. As any teacher or parent can tell you, the difference between a 79 and an 80 isn’t a point. It is a chasm. An 80 feels good. An 80 feels like you accomplished something. A 79 just seems not quite good enough. And a 72? Well, it’s better than failing, but, especially for an 8th grader taking the exam, it will likely feel like failing it.

So, what did it take to get an 80 on the old Integrated Algebra exam? Right around a 60%. So, a student who knew 60% of the credit on the older Algebra exam felt like they got a good grade. What did a student need on the June 2014 Common Core Algebra I exam, to get an 80? Well, they basically needed an 80. It was actually a 78%, but that’s splitting hairs. Here’s a graph that shows all of this:

Comparison Chart #1

Now, the Common Core conversion curve has real mathematical problems (which leads to political problems as well). Think about this for second:

35% raw = 65% scaled

80% raw = 80% scaled

Why is this a problem? Well, try to cram 45% of the raw score scale (35% to 80%) into only 15% of the scaled score scale. That leads to all sorts of problems. For instance, a kid who scored a 47 out of 86 points earned a scaled score of 72. But a kid who scored a 58 out of 86 earned a scaled score of a 75. That second student scored 11 points more (its actually 13% points more) than the first student, but only went up 3 percent points. What????

But, the real issue that many, many schools faced were kids who did quite well during the school year, many of them advanced 8th graders, and then scored a 78, a 75, or maybe even as low as a 72 on the Common Core Algebra I exam. But, how bad is that 72? Well, a 72% on the June 2014 CC Alg I exam corresponded to a raw percent of 58%. What would 58% raw earn you on the Integrated Algebra exam? Oh, right around an 80% scaled.

So, a little “scale maintenance” was certainly in order. And, boy did they do some!!! Let’s start with the most important number, the raw percent needed to pass. For comparison:

June 2014 Integrated Algebra exam: 35% raw score needed to pass

June 2014 Common Core Algebra I exam: 35% raw score needed to pass

June 2016 Common Core Algebra I exam: 31% raw score needed to pass

So, they lowered the percent needed to pass. To give you some perspective, it basically means a student could miss two additional multiple choice questions and still pass. But, now the question of the 80. Again, the comparison:

June 2014 Integrated Algebra exam: 59% needed to scale to an 80%

June 2014 Common Core Algebra I exam: 78% needed to scale to an 80%

June 2016 Common Core Algebra I exam: 59% needed to scale to an 80% (sound familiar?)

Here’s a graph to show all three conversion curves:

Comparison #2

What’s fascinating is that they basically took the two June 2014 curves (red and blue) and spliced them together to create the one for this year (green). Notice how the green curve basically follows the red curve (the June 2014 CC Alg I exam) until the pass mark. Then, it follows the more traditional Integrated Algebra curve the rest of the way.

There are a lot of thoughts I have on all of this once I get past the math itself. My initial thought is how arbitrary it all seems. Right? It used to be that a kid who got an 82 got an 82. But, not anymore. My second thought is that there can now be absolutely no comparison that schools can make to previous year results. You could really only compare raw scores. The scaled scores are meaningless in year over year comparisons. Finally, given that all of this is arbitrary, it certainly seems like this is another case of what I’ve now decided to dub Lake Wobegon Syndrome.

We want our kids to learn more, we want them to be more challenged, but when they don’t live up to those challenges, then we change the metric that we use to make it seem like all kids are above average. But, the plain fact is, with an arbitrary scale such as this one, as a society we can manipulate the results in any way that we want to show any result that we want. So, what is the point exactly? And, how will we really know if our kids are actually learning more math if we can’t even agree on how to measure their progress?

Don’t misconstrue my commentary. I applaud that NYSED listened to voices of parents and teachers around the state and changed the conversion curve. Many students who worked very hard for the last two years felt like complete failures whereas if they had taken math a few years prior, they would have had scores in the 80’s. So, I think this is an excellent start. But, I still think it opens a lot of questions. I will also be extremely curious to see what the curves look like on Common Core Geometry and the brand new Common Core Algebra II.

For now, I need to go watch some soccer! Go U.S.A.

Posted on

Standards Documents

On our old site we gave access to an annotated table of contents that had the PARCC EOY standards mapped to each individual lesson. We also had the lessons mapped to the standards. We’ll get both documents back up, but I thought I would post them here just to have them on the site.

Table of Contents Annotated with PARCC EOY Standards

PARCC EOY Alignment with Common Core Algebra I by eMathInstruction