The Parole Officer’s Check List, the Dialectic of Competition, and Gnarly Problems

Editor’s note: This is the fourth piece in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California.  He has written articles on math education that have appeared in The AtlanticNonpartisan Education Review, Education NextEducation News and AMS Notices.  He is also the author of three books on math education.  Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd.” The previous chapters can be found here:  Chapter 1 , Chapter 2 , Chapter 3.

4. The Parole Officer’s Check List, the Dielectic of Competition, and Gnarly Problems

Upon starting at St. Stevens, I had completed my two years compulsory Teacher Induction Program (TIP) under two different parole officers, otherwise known as mentors. The TIP process consisted of discussions, observations, and the mentors/parole officers having to fill out an online checklist of items which would serve as the final authentication of having gone through the induction.

My first mentor (who I will call Ellen) told me that she would be making suggestions and giving me ideas, but I was under no obligation to follow any of them. This was good because she had no shortage of dubious ideas and quickly learned that I was going to do things my way. At one point early in our meetings, having determined that I didn’t assign group work and rarely had activities, Ellen asked “What are you going to do about Common Core, which requires activities and group work in teaching math?”

“The Common Core standards do not prescribe such pedagogy,” I said and pointed out that the website for Common Core states clearly that the standards do not mandate pedagogical approaches. I expected an argument, but instead she quickly moved on to other business. The mentors are used to teachers fresh out of ed school who are in their twenties and believe whatever they’ve been told about how to teach and what Common Core requires. In any event that was one response she did not expect that remained unrecorded on the online checklist.

My second mentor, who I will call Diane, was assigned during the second year of my induction. Like Ellen, Diane also had teaching experience—second grade mostly—and was now in charge of the mentor/parole program for the county in which I teach. Like Ellen, she would make suggestions that I could either follow or ignore. She would occasionally evince educational group-think that passed as sound advice. 

Our first meeting took place in my classroom. “Tell me about your classes,” she said.

I had two that year: a seventh grade math class (non-accelerated), and eighth grade algebra—the latter made up of students I had taught the previous year.

“My seventh grade math class had a rough year last year so they’re coming in with an ‘I can’t do math’ attitude right at the start,” I said.

“That’s never a good thing,” she said.

 “And on top of that, they have significant deficits. Like not knowing their multiplication facts.”

Her eyes widened. “Really? How can that be?”

Actually, it can be and is in many schools across the US. I wondered how on earth she could not know this, being in education as long as she had.

“So how are you addressing that?” she asked.

“I’ll let you in on a secret,” I said.  She looked intrigued.

“I’ve been giving them timed multiplication quizzes every day to start off the class. My principal told me that timed quizzes stress students, but these kids love the competition, plus I show them how their scores are increasing.”

“Of course!” she said. “Kids love to compete.” I was heartened at this for two reasons: she wasn’t against memorizing multiplication facts, and she appeared to be going against the educationist dialectic of “competition is bad”. But then she added, “Of course, it isn’t good to do that in the first and second grades because it can stress kids out, but it’s perfect for seventh graders.”  A few minutes later when I told her I posted the top three scores on quizzes or tests, the dialectic clicked in.

“Are you sure that’s a good thing to do? Some of the students who didn’t make the top scores might feel left out,” she said. 

“They ask me who got the top scores, and they don’t seem upset when I post them, so I’m assuming it’s OK,” I said. She had no answer to that and looked around the room.  “I like the way you’ve set up your classroom.”

Diane liked various quotes I had tacked up on my walls; random things uttered by my students that I felt worthy of posting.  Like “I never get used to math; it’s always changing.” and “Variables don’t make sense and make sense at the same time”.

I kept the ones from my previous year’s classes on the wall, as well as those from my current students. “Seeing quotes from previous classes gives students a sense of legacy and tradition,” I said. I remember being intrigued when my seventh grade English teacher would show us examples of work done by her previous classes, and we would see the names of students from years past—some were brothers and sisters of my classmates.

I pointed out one quote from a student named Jimmy in my current seventh grade class. It had emerged from a dialogue I had with him on subtracting negative numbers:

Me: You lose 5 yards on a play.  You have to make a first down.  How many yards do you have to run?

Jimmy:  Couldn’t you just punt it?

Jimmy had had a particularly rough time in math the previous year and had very little confidence. The first time we had a quiz I had made sure that the students would do well, giving them lots of preparation. Jimmy did do well: 97%. When I was handing back the quizzes he kept saying “I know I failed it.” When he saw his quiz he was silent and then asked if anyone in my class last year had failed.

“No,” I said.

“Do you think it’s possible that I’ll pass this class?” he asked.

“Yes, it’s entirely possible,” I said.

I told Diane about this. “Fantastic that he got 97%. How did that happen?”

I explained how I was using JUMP this year and how it breaks things down into manageable chunks of information that students could master. Given where they were coming from I felt that building up their confidence was very much needed.

“Are you planning to go beyond just mastery and give them some gnarly problems?”

I was tempted to ask her to define “gnarly problems”, though I’m fairly sure it had something to do with “If they can’t apply prior knowledge to new problems they haven’t seen before, there is no understanding”. But my answer to her was “Of course”. JUMP does in fact provide “extension” problems in the teacher’s manual. I made a note to self which when roughly translated was something like: “Come up with something.” Given the deck I had been handed with this class, I had other things on my mind besides giving the class gnarly problems, however it was being defined.

Understanding, and Outliers in a Sea of Outliers

Editor’s note: This is the third piece in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California.  He has written articles on math education that have appeared in The AtlanticEducation NextEducation News and AMS Notices.  He is also the author of three books on math education.  Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd.” Chapters 1 and 2 can be found here and here.

3. Understanding, and Outliers in a Sea of Outliers

During my second week of school at St. Stevens the principal, Marianne, called me in to her office to tell me some good news.  “I just want to let you know that we heard from Mary’s mother and that Mary said she is really happy in your class; she says that “Mr. Garelick really wants us to understand.”

I was glad to hear that Mary’s mother was pleased, and while I haven’t taught for very long, I knew enough not to believe I was any kind of miracle worker—particularly during the first few weeks at school when everything is new and has the cast of a halo over it. At my previous school during back-to-school night one year before, a parent of one of my students in my seventh grade class said something similar. “My son said that this is the first time in any math class that he actually understood the math.”

In both cases, it didn’t hurt that the word “understand” was used in conjunction with my teaching, although the word has different meaning for me than what others in education think it means. I want students to be able to do the math. That’s pretty much what students mean when they say they understand. It isn’t something I obsess over.

Mary was one of two girls in my eighth grade math class (Math 8), who had to come in twice a week for intervention help for half an hour before classes began. The other student was Valerie who had been classified as special needs since the lower grades. They were both very animated girls; Mary was very outgoing and friendly with me. Valerie was more guarded. In her world of Smart Phone, songs, reality TV, I felt she viewed me as frightfully out of touch with what was really important. Math was certainly not on her list.

My Math 8 class was similar in some ways to my last year’s seventh grade class. My prior school, like St. Stevens, had two seventh grade math classes—one accelerated, the other not. I taught the non-accelerated group who considered themselves “the dumb class”. Their doubts were compounded by their last year’s math teacher who was not popular with parents or students, and was finally let go by the school.  My Math 8 class similarly knew they didn’t make the cut for the eighth grade algebra class (which I was teaching). Their previous math teacher was similarly unpopular—and also let go by the school.

In a school as small as St. Stevens, there weren’t enough students to form a remedial class by itself. As a result, in the midst of a class in which the students already doubted their abilities, Mary and Valerie felt they were outliers. I worked with them as best as I could. I called on them infrequently in the main class, and focused on them during my intervention time.

At first, I tried to get them up to speed with what the rest of the class was doing. During one of my sessions with them, I went over one-step equations. I asked them to solve the equation 6x = 12.   I had reached the point where neither one was trying to subtract the 6 from 6x  to isolate x. But while Marie understood that 6x meant 6 multiplied by x , Valerie could not see that; nor could she see that solving it meant undoing the multiplication by division.

“How do we solve it?” I asked.

 “You put the 6 underneath both sides,” Valerie said.

That is:

Putting one number underneath another meant divide to Valerie which is as procedural-minded as you can get. If ever pressed to justify my acceptance of her level of understanding to well-meaning doing-math-is-not-knowing-math types I could say that her method at least incorporated the concept that a fraction means division. No one ever asked, but just to make sure, I said “And what do we call the operation when we put another number ‘underneath’ another?”

She thought a moment.

Mary whispered in Valerie’s ear: “Division”.

“Oh; it’s division,” Valerie said.

Over the next few weeks, I worked with the two girls privately while trying to keep them on track in the Math 8 class. I realized that their deficits were so significant that to hold them to the standards of Math 8 would result in failure. Katherine, the assistant principal agreed with me, and said to focus instead on filling in the gaps and to base their grade on their mastery of those.

I leveled with them one morning when they came in for their intervention.

“The Math 8 class must be extremely painful for you,” I said.

Valerie for the first time let down her guard.  “I just don’t understand what’s going on.”

I found her statement true in a number of ways.  One was just the fact that she admitted it. But more, it brought home the issue of understanding. Of course she didn’t understand—she barely had the procedural and factual tools that would allow her even the lowest level of understanding of what we were doing.

While there are those who would say “Of course they didn’t understand; traditional math has beat it out of them,” such thinking is so misguided that, in the words of someone whose name I can’t remember: “it isn’t even wrong”. In the case of Valerie and Mary, they needed more than the two half-hour interventions every week. They needed someone who specialized in working with what is known as dyscalculia. But qualifying as a special needs student doesn’t guarantee the student will get the kind of help to deal with a disability.

They had finished what I gave them to do early that day, and Mary being in a celebratory mood said the two were going to make a drawing for me. They giggled while they drew a rather strange looking bird laying eggs and eating blueberries among other odd things going on and presented it to me.  I put it on the wall where it remained for the entire school year. Sometimes other students would ask what the drawing was, and they would explain it, excitedly.  The excitement was partly due to them having drawn it, and partly due to my keeping it on the wall for all to see.

Changing State Standards: Repeal, Revise, Replace, Rebrand, Update, or Unique?

Issues related to and surrounding the Common Core State Standards (CCSS) are controversial and “toxic” (as Mike Huckabee put it) for many people both in and outside of education, including decision-makers.  Rather than truly replacing the CCSS, some states have simply rebranded them.  As a result, “College and Career Readiness Standards” and setting “higher” national standards are viewed as euphemisms for the CCSS.  Rebranding has taken many forms, from simply changing the name to having committees review the standards, make minor, unsubstantial changes, add some front material, and possibly reformat their presentation.

For those familiar with pre-CCSS state math standards and who can compare them with the Common Core State Standards for Mathematics (CCSS-M), it can be seen the CCSS-M are uniquely written.  Once familiar with this uniqueness, a person can usually determine if CCSS-M standards have been used as a base or model for a standards revision or rewrite.

Two states, Alabama and Florida, have been making noise about getting rid of the Common Core State Standards.  Some headline terms used include repeal, end, ditch, eliminate, and scrap.  As time goes on, more states will consider changing their standards.  It will be interesting to see how they go about it and what the resulting product (set of standards) looks like.

Here are some possible scenarios of what states might do as they consider changing their CCSS-M standards.  These are listed from worst to best case

  1. Adopt the Common Core State Standards as they are
  2. Rebrand the CCSS-M in name only
  3. Rebrand CCSS-M in name with minor changes*
  4. Rewrite standards using CCSS-M as the model**
  5. Rewrite standards using another state’s weak pre-CCSS standards as a model
  6. Rewrite standards using an A rated set of pre-CCSS standards as a model
  7. Adopt an A rated set of pre-CCSS standards (INCA, or even the unrated WEMS)

*changes some states made, even minor ones, significantly weakened their standards

**this results in standards that are basically CCSS with phrases that have been rewritten

I would recommend states work to avoid paths 1 though 5 and if possible and only accept paths 6 or 7.

Some states have expended a lot of resources on rebrands or rewrites that have resulted in adopting a set of standards that in essence are the CCSS (or worse).  It doesn’t appear that any state completing a rebrand or rewrite has done anything that actually improved the CCSS.

One strategy that has been used in a few states is to have a survey set up for the public to provide specific input on the current standards, often standard by standard.  This strategy will mostly result in a set a standards that closely resembles or is the same as the current standards.  And if the current standards are the Common Core or a rebrand a brand makeover results.  This strategy fits with path 4 where the standards are rewritten using the CCSS as a model.

Do states that make noise about the CCSS want to repeal, revise, replace, rebrand, or update their standards?  Do they really want to have a better set of standards?  Or do they just want to make noise having people think they are doing something that will result in a better set of standards when the real result will be little to no change or something worse?


An espresso-based job interview, a 1962 algebra book, and procedures vs understanding

Editor’s note: This is the second piece in a series called “Out on Good Behavior: Teaching Math While Looking Over Your Shoulder” by Barry Garelick, a second-career math teacher in California.  He has written articles on math education that have appeared in The AtlanticEducation NextEducation News and AMS Notices.  He is also the author of three books on math education.  Says Mr. Garelick: “At its completion, this series will be published in book form by John Catt Educational, Ltd.” The first piece can be found here.

An espresso-based job interview, a 1962 algebra book, and procedures vs understanding

In the remaining two weeks at my previous school, I applied for the few math teaching positions that were advertised. I had the typical non-responses except for one—a high school that specialized in problem-based learning. I had applied there out of desperation never expecting a response. I received an email saying they were interested in interviewing me. Despite my skills at making my teaching appear to be what people wanted to see, I knew that this one required too much suspension of disbelief on both sides of the aisle.

I cancelled the interview saying something along the lines of having to wash my hair that day. Shortly after that, I received another email from St. Stevens, a K-8 Catholic school needing a part-time math teacher. A fellow math teacher from another school had put in a good word for me. Like the school where I had been, this school was also part of a small community and had about two hundred students.

A few days later I was at the school for a 2 PM interview. I tend to get a bit logy in the afternoon so I thought I’d have an espresso prior to coming in. The principal, Marianne and assistant principal, Katherine, interviewed me and asked the usual questions: What does a typical lesson look like, what are my expectations and so on. My inner voice tried to keep me from extended caffeinated responses.  I emphasized how I leave time for students to start on homework in class, do the “I do, we do, you do” technique, and in my controlled ramblings managed to get across that I am, by and large, traditional.

But when the assistant principal asked me what my approach was in teaching algebra the espresso kicked in big time and my inner voice was having a hard time keeping up. I said that I taught using a 1962 algebra textbook by Dolciani. 

Inner voice: “You shouldn’t have said that.”

“I bought about fifteen of them over the internet when they were selling for one cent a piece about four years ago. So I was basically paying for shipping. But now the prices increased because of Amazon’s supply and demand algorithm, so they’re selling for about $60 a copy last time I looked. Which tells me a lot of people are buying them.”

“Please shut up.”

I talked about how I liked the sequence, structure and explanations of Dolciani’s book much better than the official textbook. As it turned out, so did the students despite the increased amount of word problems—and the word problems were yet another plus for using the book.

“But did you cover what was in the Common Core standards?” Marianne asked. I assured them that I did, supplementing with topics that weren’t in Dolciani, like exponential growth and decay.


I hastened to add that I did not spend inordinate amounts of time on exponential growth and decay functions.


“Did you cover exponents at all?” Katherine asked. “Because students generally are weak on those.”

“You mean like products and quotients of powers? Oh yeah, big time. The Dolciani book is very big on those.”  I was about to repeat that I didn’t spend time on exponential growth and decay, but the caffeine was mercifully wearing off.

They did not seem perturbed by any of my ramblings. Then again, it was during the last week of school and I imagine that they were so exhausted that they were probably amenable to anything I said.

They asked about my classroom management techniques. In any interview or evaluation process, one has to have some weakness to talk about and I freely admitted that classroom management is not my strong suit. I mentioned that my seventh grade math class had behavior problems even though there were a total of 10 students in the class.

“How did you handle the problems?” Marianne asked.

“I had a warning system; two warnings and they got a detention.  I wasn’t too faithful in carrying that out though.”

“Why was that?”

“When I gave a detention, the two main troublemakers were really good at carrying on about it and crying.”

“They cried?”

“I hated giving detentions. I always got talk-back, like ‘But I wasn’t talking’. And then the crying. Which they did with all the teachers, I found out.”

“So how did you deal with them most of the time, then? What did you do?”

I explained how this group had large deficits in math skills and most of the boys in the group had given up at believing they could learn math.

“I used an alternative textbook, which my school let me use: JUMP Math. It was developed in Canada and broke concepts down into very small incremental steps. It scaffolds problems down to incremental procedures and builds on those.”

I went on about how procedures can lead to understanding and you can teach understanding until the cows come home, but most students are going to grab onto the procedures.

“Did it work?” Katherine asked.

“Well, let’s just say that it would have been even worse had I not tried to fill in their deficits.”

They had no response and then the usual niceties ensued and the interview was over.

They called my references, as well as the principal of my school as I found out the next day. “Marianne called me about you.  She sounded excited,” the principal told me.

“What did she ask?”

 “She wanted to know more about the seventh grade class; she was curious about their behavior.”

“Oh,” I said. “I thought she might.”

“I told her they were really a tough bunch of students but you handled them well.”

“Did she ask about the algebra books I used for my algebra class? Or about procedures versus understanding?”

“No; just about the seventh grade class,” she said. “She sounded positive.”

And a few days later I was offered the job at St. Stevens.  “I think you’ll like it there,” the principal told me. 

I hoped so. There are always doubts about starting any new job, particularly in teaching. I had given them fair warning in the interview about how I taught. I hoped I would be allowed autonomy, but for the most part, I was glad they brought me in out of the rain.

Teacher Incompetence or Lack of Adequate Training?

The research is mixed. Some reviews (of the many studies on retention or promotion) have shown little benefit for retention in grade 3 compared with social promotion to grade 4.  For example, a 2017 review looked at the results of Florida’s “A+ plan,” begun by Jeb Bush when he was governor. Little benefit has been found for the retained students.

Other reviews have shown that retention in the primary grades correlated with dropping out in high school. Nevertheless, some students who don’t pass a grade 3 reading test (for promotion to grade 4) do go on to grade 4 after submitting a portfolio, taking an alternative assessment, and/or attending a special summer school session and thereby qualifying for promotion to grade 4, even though they still may not do grade 4 work adequately.  The quality of the work these low achievers do may depend on whether upper elementary teachers can group them for skills work in their self-contained classrooms.  School or state policies may forbid grouping practices in the teaching of reading, especially in elementary school.

Unfortunately, neither promotion nor retention has solved the problem of low reading achievement, it seems.  Earlier intervention than grade 3 is now often recommended. For example, see a 2008 review. However, it is not clear if earlier intervention has helped poor readers in grades K, 1, and 2 to pass a high-stakes grade 3 reading test or graduate from high school at a more frequent rate compared with a similar group of poor readers without early intervention or help in school. For example, see this recent review. As we all know, there are many low achievers in elementary reading classes to this day.

Indeed, because of a growing number of state laws requiring retention (probably in desperation), many third graders in this country’s schools today will not be promoted to fourth grade.  For example, we are told that thousands may be held back in Mississippi. That newspaper article from Mississippi refrains from pointing a finger at anyone—the students or their teachers or parents.  However, many education policymakers seem to fault, implicitly at least, elementary classroom teachers for the failure of many kids to learn how to read by grade 3.

So-called “retention” studies also seem to assume teachers or school policy makers are to blame when researchers find few long-term differences between low-achieving third graders who repeated grade 3 and similar low-achieving third graders who were promoted to grade 4. Researchers as well as journalists, nevertheless, are reluctant to criticize struggling students or their teachers.  

But when a large group of kids in a state have not learned beginning reading skills by the end of grade 3 (remember, they’ve been in school for at least 4 years), it is fair to ask if the problem may lie with their teachers’ training programs, not their teachers. Few parents or other readers would guess that teachers’ training programs may be the source of the problem because the studies on retention in grade 3 rarely provide information about the beginning reading program these students have had or the preparation program their teachers had.   Their focus is on students’ achievement in school after grade 3.

Why are large numbers of students who don’t pass a grade 3 test of beginning reading apt to be an indictment of a state’s preparation programs for primary grade teachers?  Because, as I learned in Massachusetts, most elementary teachers have not been trained to use effective, research-based strategies.  How do we know this?  I learned this by examining licensure tests for prospective teachers of young children before helping to develop one in the Bay State. Most licensure tests of beginning reading knowledge for prospective teachers of young children, I discovered, do not assess or assess adequately the major elements of research-based knowledge of beginning reading as set forth in the National Reading Panel’s report of 2000

The components of effective beginning reading programs and strategies one would expect researchers to look for, or professional development providers to provide, are well-known and listed here. But, alas, they are not apt to be found in many primary classrooms.  Teachers teach the way that they are taught to teach in their training programs.

Since around the 1960s, teacher training programs in the U.S. have tended to promote guessing from context (often called Whole Language) as the primary strategy.  Even if some decoding is taught (as in many misnamed “Balanced Literacy” programs), kids are not taught the purpose for an alphabet. Nor are they taught systematically how to decode the alphabetic symbols used for beginning reading in English (the symbols for the sounds made in words read by children in the short stories created for beginning readers). Yet, somehow, teacher preparation programs have escaped the (often implicit) fault-finding that their own students—prospective teachers—have not.  For reasons that are not clear yet, low achievement in K-12 students is perceived by education policy makers, researchers, and many others as the fault of their teachers.  At least, that is who the framers of the Race to the Top grant competition in 2011 decided should be held accountable for low K-12 student scores on federal or state-mandated achievement tests.  Indeed, sometimes as much as 50 percent of a teacher’s evaluation is based on her students’ test scores.   

Strangely, while K-12 teachers, under current education policies, are held accountable to varying degrees for the low scores of their K-12 students, faculty in teacher preparation programs are NOT held accountable for the failure of their own students (the prospective teachers they recruited and prepared) to teach K-12 reading well enough so that the racial and ethnic “gaps” between low-achieving K-12 students’ average reading scores and the average reading scores of higher-achieving K-12  students have narrowed.  What is worse, many education policy makers seem to believe today that the chief reason low-achieving readers are low-achieving is because their teachers, principals, or communities are bigoted and have discriminated against them.  

One might think that the requirement to pass a well-constructed licensure test in beginning reading skills for all prospective teachers of young children would ensure that all young children in our schools have adequately trained teachers.  But only a few states (Massachusetts, Arkansas, Connecticut, Mississippi, New Hampshire, North Carolina, Ohio, and Wisconsin) today seem to use a well-constructed licensure test of beginning reading skills for prospective special education, early childhood, and/or elementary teachers, as I showed in my own research on the content of licensure tests for special education teachers.

Moreover, it turns out that in some states there are differences in pass rates for “white” and black prospective teachers on their required licensure tests in reading, leading some policymakers and researchers to imply that racial or ethnic differences in pass rates for prospective teachers also means discriminatory tests (licensure tests).

For example, in Wisconsin: “According to Department of Public Instruction (DPI) records, two-thirds of people who took the Foundations of Reading Test (FoRT) between 2013 and 2016 [a test developed in the Bay State in 2000] passed on the first try. Including those who took it two or more times, 85% passed. Pass rates were better for white test-takers than for minority test-takers, which led to concerns that the test keeps a disproportionate number of minority potential-teachers out of classrooms. Department of Public Instruction officials say many who have not passed FoRT would be good teachers and passing FoRT isn’t the only sign someone will be a good teacher.”

A major part of the problem with the thinking expressed by education policy makers at the Wisconsin DPI is the idea that raw scores on licensure tests predict teacher effectiveness. They weren’t intended to do so at the inception of teacher licensing, and still are not.  Passing a licensure test in most if not all professions means only that the test-taker has adequate entry-level knowledge for the profession.  It is assumed that those who don’t pass the test don’t get a license.  While adequate entry-level subject knowledge is needed for effectiveness in any profession and is necessary.  But it is not sufficient.  For prospective teachers of young children, student teaching experiences are expected to indicate to supervising personnel whether the test-taker is apt to become an effective teacher.  In other words, NOT passing a well-constructed licensure test of beginning reading skills is a sign that the test-taker is UNLIKELY to become a good or effective teacher of beginning reading. 

It is therefore not surprising that thousands of children across the country fail a reading test at the end of grade 3 when the basic problem may well be that they have not been taught how to read by their teacher because she has not been trained in her preparation program to use research-based knowledge of beginning reading, or tested for this knowledge on her licensure tests. This may well be the case in Florida today despite almost two decades of the A+ Plan.