Sunday, June 19, 2016

Not My Father's Math Class

Today is June 19th. Even though today is Sunday, my plan was always for me to make my first summer post today, mainly because today is a holiday. And no, I don't mean Juneteenth (the holiday I mentioned when explaining why we had three extra days to file our taxes in April) -- of course I'm referring to Father's Day.

I rarely mention my family here on the blog. Except for right after my grandmother's passing, I chose not to write about family here on the blog. But today on Father's Day, I must mention my father, because he is a retired teacher. A list of influences on me as I embark on full-time first teaching job would be incomplete if I left my father off.

He was a fifth grade teacher for a few years (including the year that I was a fifth grader), until he switched to a sixth grade classroom in LAUSD. The district often had multiple-subject teachers, including my father, teach sixth grade math and science.

The summer after I graduated from high school, I was a volunteer in my father's classroom. At the time, LAUSD had year-round schools. Students were divided into three tracks, A, B, and C, and the students and the teachers attended school during different times of the year. My father was a C track teacher, meaning that he taught from July to October, and then again from January to April. This meant that I could volunteer in his classroom the entire summer, from July all the way up to my first day as a UCLA student in late September, as UCLA has a quarter college calendar.

I remember my first day in my father's classroom. I was so surprised to see how tiny the sixth graders were -- amazing considering that 13 years earlier, I'd thought that sixth graders were grownups! (I explain why I'd believed that in my June 9th post.)

Most of my volunteer work in that class was limited to helping my father grade papers. Still, I recall a few things about the way he taught his class:

-- Every third test, he would drop the lowest test grade. Therefore, he tried to give six tests per semester each in math and science, so that he could drop the two lowest test grades.
-- All tests were open-book. Despite these concessions, many students were earning D's and F's, especially in the math class.
-- The four remaining tests were the entirety of the students' grades. In particular, any homework assignments were extra credit. I wrote earlier (in my June 9th post) that I would write about the homework debate (or "debacle") soon -- well, this is the post in which I'll discuss it.
-- I remember once when a student forgot to bring his pencil to class. My father told the student that he was just like a baseball player who went up to home plate without a baseball bat! Just as it would look silly for a player making millions of dollars to forget to bring a bat to the plate, that's how silly it is for a student to forget his or her pencil.
-- My father regularly gave out candy as a reward/incentive.
-- My father often said that the motto of the class was, "If you don't know the answer, at least know where to find it." In many ways this statement applies more to science than to math -- in math one must calculate the answer, but in science all the answers should be right there in the text.

This, in fact, reminds me of my very last subbing assignment. On June 2nd I subbed in a math class, but the following day I was actually in a science class. (At the time, I didn't mention it on the blog because it had nothing to do with math.)

It was a seventh grade lesson on the human reproductive system. Due to the explicit nature of the material, students required parental permission in order to attend the lessons. Most likely, the teacher would send students without a permission slip out of the classroom, but she obviously didn't want a sub to deal with all of that. So instead, she provided an alternate packet for the students who didn't have parental permission to study the main lesson. Her expectations were that all students would work independently on their respective packets.

Now in two of the classes, the teacher's lesson plan worked. Again, these classes weren't labeled as "honors" classes, but it was obvious that the teacher expected more from those students -- their packets included an extra vocabulary page.

But in the non-honors classes, the students refused to work on their assignments. Their excuse was, "Normally, the teacher explains it to us." Thus many of the students left more than half of their worksheets blank -- and those who had been absent at least once that week left even more blanks.

In those classes I had more pressing issues to deal with -- including the fact that an explosive device was found in the classroom! But if I could have focused only on the academics, I would have told the students my father's motto: "If you don't know the answer, at least know where to find it."

Notice it's likely that what the students said was true -- usually they wait for the teacher to explain things on their worksheets, so when there is no one to explain anything, they do no work. And after an absence, the students wait until the teacher has a spare moment to tell them what they missed -- until then, they do no work. The teacher probably would have told me to help the students out with the worksheet -- except that she couldn't because of the parental permission problem. She didn't want me to deal with students would had to leave the room and she didn't want me to start discussing the material out loud in front of the students who didn't have permission. I might even have played the "Who Am I?" game to motivate the students to work, except that I couldn't speak out loud.

There were two issues in that class -- the sub issue and the parental permission issue. Had there been only one issue or the other, there'd have been no problem. It was the combination that doomed the class -- the teacher just hoped that the students would work independently, but they didn't. That's why I wished I could have given them my father's advice -- "If you don't know the answer, at least know where to find it." Maybe then, the students would have realized that they were to search for the answers in their science text.

Now that I have discussed my father's class, I ask myself, can I apply any of my father's teaching methods to my own classroom? Well, my new classroom is making some changes that will make my class very different from the one he taught.

First of all, the school has changed its bell schedule. It is very different from the one that I mentioned last month (in my May 11th post), when I was trying to explain what a block Then again, I did say that apparently, there are as many block schedules as there are block schools!

-- The block days still go Monday/Thursday and Tuesday/Friday. But now there are three blocks that are 80 minutes in length, followed by a 60-minute period. Fifth period, at the end of the day, is 30 minutes and is reserved for P.E. class.
-- Wednesdays are still Common Planning days. Four classes meet for 50 minutes each, and then fifth period P.E. is 25 minutes.
-- Since I said that this blog will focus on my eighth grade class, let me state here when I will see my eighth graders. They will meet me during the second block on Mondays and Thursdays and the third block the other three days. Of the three grades, eighth graders have the longest math blocks, as this is a critical year in math -- the year before Algebra I in high school.

I said that I would post to this blog everyday that 8th graders meet. This means that I'd still be posting everyday -- which will be tough since I have three preps! Then again, I also promised that I would post three times a week -- and that promise is more manageable. So expect me to post three times a week during the upcoming school year.

The school year at my charter school will be same as the underlying district, LAUSD -- except for one day that is different in the spring. I'll explain the one difference when we reach it. The first day of school will be on August 16th.

Now here's the biggest change -- the math curriculum. Previously, our school used the McDougal Littell text. I discussed this text here on the blog -- I bought an old 2001 edition of the seventh grade text for $2, but this was a more recent 2008 edition.

But a few schools in the LAUSD were selected to use a new STEM-based curriculum -- and my charter school chose to go along with it. This curriculum is called IMaST, and it was developed at Illinois State University. (What is it with the Prairie State and math curricula? I spent the first two years of this blog discussing the U of Chicago text, and now I'm moving on to Illinois State!)

Let me warn you now -- if you're a traditionalist, you're not going to like the Illinois State text. To see why, let's compare the old McDougal Littell text to the new Illinois State text.

First, here are the unit names in the McDougal Littell seventh grade text:

Unit 1: Number Sense (Chapters 1-4)
Unit 2: Algebra and Functions (Chapters 5-7)
Unit 3: Measurement and Geometry (Chapters 8-10)
Unit 4: Statistics, Data Analysis, and Probability (Chapter 11)
Polynomials: Review and Preview (Chapter 12)

This seventh grade text was published in 2008 -- the last year before Common Core, and so the text is based on the old California State Standards. These standards expected eighth graders to take Algebra I, and so seventh grade was a Pre-Algebra course. Except possibly for Chapter 11, we expect traditionalists to be satisfied with the old text.

Now let's look at the unit names in the new Illinois State seventh grade text:

Tools for Learning
Unit 1: Mathematics in Shapes
Unit 2: Mathematics in Sustainability
Unit 3: Mathematics in Nutrition
Unit 4: Mathematics in Flight

And now the traditionalists are wondering -- what? Where are the rational numbers? Where exactly is the Pre-Algebra? At this point, they'd take statistics over "sustainability." Except for "shapes," which is sort of like geometry, this table of contents doesn't inspire traditionalists one bit.

You see, the name IMaST stands for "Integrating Mathematics, Science, and Technology." This is essentially project-based learning -- students divide into groups and work on various projects that incorporate both math and science.

Since the focus of this blog is eighth grade, let's look at the Illinois State text for eighth grade in much more detail:

Tools for Learning:
1. The Need for Speed
2. Show Me the Numbers
3. What's the Best Advantage?
4. Learning to Communicate

Unit 1: Mathematics in Settlements
5. H20 + ? Measuring Using Parts Per Million (ppm)
6. The Capacity of Water-Carrying Structures
7. Shapes, Angles and Structures: How Strong Is It?
8. Tessellate a Structural Design: A Study of Polygons
9. Similarity

Unit 2: Mathematics in Systems
10. Input, Process, Output...Does It Work?
11. Bouncing Balls
12. Say it with Words, Pictures, Tables, and Symbols
13. Looking at Relationships
14. Where shall we Meet?
15. That Model Looks Good!
16. Atmospheric Layers

Unit 3: Mathematics in Animal Habitats
17. Give Me Space
18. Patterns in Data
19. Chances Are

Unit 4: Mathematics in Communication
20. Sound Waves
21. Codes I
22. Codes II: Tracking Data
23. Codes III
24. Matrices I
25. Matrices II

In many ways, this is similar to Morris Kline's book that we discussed on the blog throughout April and May -- the emphasis is on how the math is used, not what type of math it is. So the title of each "module" (called a "learning cycle" in this text) is an application.

This text is full of projects, right from the very beginning. In fact, the first project, "Off to the Races: Design and Make a Car" (made out of cardboard) starts on page 3.

We already know that traditionalists would definitely dislike this approach to teaching. But actually, there is precious little mention of Illinois State or IMaST on any traditionalist website. One of the oldest traditionalist websites around is called Mathematically Correct:

Try to obtain choice. My main concern about these programs is that, in an effort to keep everyone entertained, they tend to turn off the good students who would do well if given the traditional math. Try to keep the traditional approaches around as an option. This is currently an issue at several high schools in my area, which use Core-Plus (out of Western Michigan University) for all students, and at a middle school, which uses IMaST (out of Illinois State University) exclusively. By traditional approaches I don't mean just drill. There have to be applications in order to make things meaningful.

It is implied above that IMaST is a non-traditional math text -- but other than that, there's no explanation as to what IMaST is or why traditionalists should oppose it.

Meanwhile, the traditionalist Bill commented this week on an article -- no, it's not about the Illinois State text per se, but about group work in general. Of course, the Illinois State text almost certainly expects students to complete these projects in groups, so it's indeed relevant to the text.

As usual, let me link to the article first:

And here's what Bill writes on the Joanne Jacobs webpage:

Group projects usually [stink -- dw] due to the fact that usually one or two people wind up doing a majority of the work, but everyone gets the same grade…

I notice that the commenter right below Bill is "mathcurmudgeon." (This poster doesn't provide a gender, so I'll use phrases such as "the poster" or "the author" to refer to Curmudgeon in order to avoid gendered pronouns.) Curmudgeon begins by quoting a commenter from the article itself:

From Andrew Old, UK.
“If you want to learn how to cooperate effectively with others, then the last place you’d start is in a group of teenagers being made to do school work. This is like saying the best way to learn how to make pork sausages is by being imprisoned in a pig farm with a half-dozen rabbis. Putting together people who are neither experienced at doing something, or particularly inclined to want to do it, is not how you learn to do that something.”

As usual, I disagree with the traditionalists regarding the secondary grades. First of all, Andrew Old compares students who don't want to learn math to rabbis who don't want to make pork sausages. But we wouldn't force a rabbi to make pork sausages in the first place -- so the natural conclusion from Old's argument is that we shouldn't force students uninterested in math to take math at all. Is that what Old really wants to imply?

Now Curmudgeon's comment on the Jacobs site links to the author's own blog. Interestingly enough, Curmudgeon hadn't posted at all in 2016 until making seven posts in May -- almost as if the author was trying to participate in MTBoS30! Most MTBoS members aren't traditionalists -- look at the blogroll and we see that Curmudgeon links to prominent members of the MTBoS (like the king, Dan Meyer) as well as prominent traditionalist websites (such as Kitchen Table Math).

At the top of the page, Curmudgeon writes at the top of the page, which I quote with commentary:


And of course Illinois State math is all about collaborative exploration, so we already know that Curmudgeon won't like IMaST...


We know that the U.S. is an outlier when it comes to Algebra and Geometry. Most other countries -- in particular those who outrank us in math -- teach Integrated Math.


It depends on what the author means by "spiraling" here. Traditionalists often use the word to refer to arithmetic, where students are taught nonstandard algorithms at first, then "spiral back" to learn the standard algorithm. OK, I'll concede Curmudgeon that point.

One of Curmudgeon's posts during the MTBoS30 month is about integrated learning -- the same type of learning promoted by Illinois State:

This was actually referring to an article about a school that eliminated its bell schedule. My new school still has five distinct periods throughout the day. Still, we can see what the poster has to say about integrated learning:

Learning is always focused on one topic. When was the last time you attended a college class called "College Algebra and British Lit as used in Cobol programming?" Teaching at the elementary grades is cross-curricular by nature. The higher you rise, the more likely you're going to specialize. Not only is each student's course mix different but the levels are, too. One freshman may take Honors Algebra2, Spanish 3 and H.English but the other takes CP English, CPAlgebra1 and Spanish1.

Then, there's competence. I can teach Physics and any level of math

Aha -- Physics and math are more naturally allied than "College Algebra and British Lit" or any of the other strawman combinations listed here. What's wrong with having an assignment that integrates physics and math -- for example, the car design project I mentioned above?

Even within a certification area, teachers have strengths and weaknesses. Some teachers are great with Geometry and others aren't.  Calculus is beyond many and some don't have the patience for pre-algebra or consumer math.

OK, I suppose this is a valid argument against integrated math. Still, how come the teachers in the high-scoring math nations don't seem to have the "some teachers are great in Geometry..." problem?

The argument that connections can't be made in 45 minute blocks is precisely the reason many schools went to 90 blocks. Not that it helped anything.

So naturally Curmudgeon doesn't think that our 80-minute blocks would help anything either.

In return for the kid's chance to pretend to learn, the schools pretend to give them an education, whitewashing over the fact that the kids have little interest in anything and school is below "nothing" on their lists.

But if the kids have little interesting in anything, how is traditionalism supposed to help them? This is an argument that many traditionalists make over and over again. They repeatedly argue that there's no point to giving activities in class, since they won't make uninterested students suddenly interested in school. But somehow, giving them traditional individual worksheets will make uninterested kids suddenly interested in school?

Let's go back to the original comment from Bill. He laments that with group assignments, students who don't care about learning will just mooch off of the harder-working students. But what would happen if those moochers were given an individual assignment instead?

The only way for Bill's argument to work is for the slackers, knowing that they can't depend on another student to do most of the work since it's an individual assignment, to be highly motivated to do the work themselves. But in reality, that doesn't happen. The slackers who depend on others to do most of the work on group assignments would just blow off the individual assignment. They'd probably throw the homework assignment away the moment they step out the door.

I believe that it's always better to learn a little bit of something than a whole lot of nothing. A student who does only a little work on a group assignment learns more than the student who does no work on an individual assignment. If a group assignment is the only way to get the students to do even a little work -- which is often the case in the secondary grades -- than so be it.

I've said it once, and I'll say it again -- I lean traditionalist when it comes to the lower elementary grades, but not when it comes to the secondary grades. But I admit that at the middle school level, some balance between traditionalist and constructivist pedagogy is best. I was not expecting a fully constructive project-based program as my first teaching assignment, but there you go. I admit that I will be learning as much as teaching this year -- I've never had to construct a race car in any class, yet it's the first project that I've been hired to teach.

Here are a few more things I wish to say about the eighth grade class: first of all, notice that the unit on geometry appears fairly early in the Illinois State text. It appears in Unit 1 -- which is not the beginning of the text, as there is a Unit 0 ("Tools for Learning"). Still, we expect to reach Unit 1 early in the year -- if not late in the first trimester, surely early in the second.

Last year, I wrote about how the Common Core expects eighth graders to derive slope from similarity, yet slope is taught before similarity in most texts. I tried to write my own eighth grade course in which similarity precedes slope, but I ran into problems. Similarity is a difficult topic, and so I didn't want it to ruin the eighth graders' first semester grades. But if I push similarity into second semester, there is less time for slope and other algebraic concepts.

I did say that I don't mind similarity earlier in the year at a trimester school, since similarity in the second trimester doesn't ruin the first trimester grades. So here at my trimester school, I will probably teach similarity early in the second trimester, before slope appears in Unit 2.

On the other hand, in my last post on June 10th, I was also thinking about how I would teach the difficult concept of statistics to my eighth graders. As it turns out, stats is split between Units 2 and 3, in the same units as slope and functions. Hopefully this will make stats easier to understand.

Each learning cycle is listed with the various Common Core Standards used in the cycle. Some Common Core defenders say that there is nothing wrong with the standards themselves, but opponents counter that the most problems are with the Standards for Mathematical Practice. For some learning cycles, the Standards for Mathematical Practice are the only standards given. This fuels the traditionalists' and Core opponents' argument that the problems with the standards run deep.

Oh, and it's finally time for me to address the elephant in the room -- homework. In fact, let's see what the Illinois State text itself says about homework, in its preface to teachers:

"Generally, the Creative Core Curriculum...does not rely on homework to reinforce what is done in the classroom. There are, however, instances where work must be completed at home. For example, in 'The Right Kind of Fuel' learning cycle, students must determine the nutritional content of various foods. The home refrigerator may be an excellent source of data. The data is used the following day in a class activity.

"The Getting the Idea section can be used as homework. Students must write out their responses requiring processes of information. In some cases, it may be appropriate to practice certain mathematics skills through drill and practice. It is likely, however, that drill and practice-type assignments will prove unnecessary as students become familiar with the learning cycle format."

We know that the traditionalists will strongly disagree with this philosophy of homework. The only homework they want to see is definitely not "get food out of the refrigerator," but exactly the drill and practice worksheets that Illinois State mentions as an afterthought, then discourages. Perhaps I'll do what my father did in his classes -- assign homework as extra credit.

We've seen that the traditionalists have very little to say about Illinois State math itself, but what do the MTBoS members have to say about it? Actually, the MTBoS doesn't write about IMaST either (unless by "IMAST" you mean a certain state standardized test in Indiana). In particular, Fawn Nguyen doesn't write about Illinois State math -- but even though she is a middle school teacher in Southern California, she doesn't reveal whether she teaches in the LAUSD (and even if she did, that doesn't necessarily mean she's at one of the schools piloting the program).

Let's compare this to what MTBoS blogger Elissa Miller writes about homework:

I have major issues with homework:
  • you don't know who actually did it
  • you don't know whether someone copied
  • you don't know whether you should 'check' or 'grade' it
  • you don't know if students understand enough to do the work alone
  • you don't know the best way to go over it without wasting class time
  • you don't know if it is effective
  • you don't know what students have to do/deal with at home
  • you don't know what other commitments/priorities students have
My normal teaching method starts with notes as a class in the INB for day one, then day two is some kind of practice activity/game, and the start of day 3 is a short quiz, then the notes for the next skill.

(And recall that the other MTBoS blogger, Fawn Nguyen, resolves to give less homework or none at all as #46 of her 51-item list.) Of course, my class will focus even more on activities and less on taking notes than Miller's and Nguyen's classes. In any case, there probably won't be much homework in my class (except for the aforementioned extra credit).

By the way, I've said that I would have to meet with the previous math teacher in order to maintain continuity for the students. Let me correct that -- I'll have to meet with the science teacher to maintain continuity, as the projects in math and science are supposed to link up. Therefore I can't really set up a pacing plan right now, as everything depends on the projects in both classes.

So I believe that I'll have much to contribute to the MTBoS, as I am perhaps the only member of the MTBoS who is teaching Illinois State math.

Oh yes, I really am a member of the MTBoS. Let's make it official with the following pledge, which I adopt from the pledge that many teachers took in January as part of the Blogging Initiative:

I, David Walker, as an official member of the MTBoS, resolve to blog three times a week during the 2016-2017 year in order to open my classroom up and share my thoughts with other teachers.

There's one thing I know as I prepare for the school year -- this is certainly not my father's math class.

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