**Table of Contents**

**1. I am a Science Teacher!**

**2. Integrated Middle School Science**

**3. Examples of New Science Standards**

**4. Fractions Yet Again!**

**5. Another Bill Comment**

**6. Fractions in the Illinois State Text**

**I am a Science Teacher!**

Now I've alluded to the NGSS several times here on the blog -- mostly in a special post I posted nine months ago in November, my Black Friday post. That post was part of the Common Core Debate, in which I discussed the pros and cons of national standards by looking a little at the science standards. But in November I took only a cursory look at NGSS, because this is a math blog and I was working on becoming a math teacher.

But now things have changed. Recall that now I am getting ready to teach using of the Illinois State text -- a text that uses project-based learning to integrate math and science together. In other words, strictly speaking

*I*And so I want to devote an entire post to the NGSS because, again, I am a science teacher, so I am

**am**a science teacher!*directly*affected by the NGSS!

Keep in mind that I still consider myself to be primarily a math teacher. And as I've been saying all summer, the blog will focus on the eighth grade class. Nonetheless, I did already warn you that this eighth grade class will contain some science projects, and I'll be writing about everything that happens in that eighth grade class -- including geometry, algebra, statistics, and science. As of now, it appears that the eighth grade class will be the largest of my three classes, but that may change as time goes on.

So let's look at the NGSS and see how it will affect my teaching. One thing to keep in mind is that currently under No Child Left Behind, all students must be tested in science once during each of elementary, middle, and high school.

Here in California, the chosen grades for the NCLB tests are fifth, eighth, and tenth grades. But this test will

*not*be the official NGSS test, but merely a "pilot test" for the new standards. My current seventh graders will take the "field test" for NGSS next year, and my current sixth graders will take the operational NGSS test the following year.

Here is a link to the NGSS as implemented in California:

http://www.cde.ca.gov/pd/ca/sc/ngssstandards.asp

Just as with the Common Core Math Standards, the NGSS for the elementary Grades K-5 are divided up by grade level, while for high school, the standards are divided by topics (as in Biology and Chemistry) rather than grade level.

But right now, I want to look at the middle school standards, since this is what I'll be teaching. As it turns out, the middle school standards are somewhat divided into 6th, 7th, and 8th grade standards, but how they are divided is very different from what you might expect.

**Integrated Middle School Science**

Back in my Black Friday post, I wrote that I wasn't sure whether California would follow the integrated pathway or the traditional pathway for middle school science. In many ways this is similar to the Integrated Math I, II, III vs. Algebra I, Geometry, Algebra II debate for high school math -- under the old pre-NGSS California standards, middle school science focused on Earth Science in the sixth grade, Life Science in the seventh grade, and Physical Science in the eighth grade.

As it turns out, the integrated pathway is now the

*preferred*pathway for middle school science. Still, the traditional pathway exists for those districts that prefer the old way. (Notice that the word "preferred" is

*not*used to describe either of the high school mathematics pathways.)

Here's a link to an old EdSource thread from last year, which debates new middle school standards for science:

https://edsource.org/2015/california-adopting-integrated-model-for-science-in-middle-grades/74814

We already know that traditionalists oppose integrated math, and so it goes without saying that traditionalists are the ones who oppose integrated middle school science.

In my new class I will be teaching science from the Illinois State STEM text. This text was written

*before*the NGSS standards, and so we don't expect the three grade-level texts to line up perfectly with either the integrated or traditional pathways. Still, it may be helpful to look up some of the projects in the sixth, seventh, and eighth text to see which pathway the projects correspond to.

For example, suppose the Illinois State eighth grade text corresponded to the old California eighth grade class -- physical science. Then we would expect most of the NGSS physical science topics to be covered in the eighth -- not sixth or seventh -- grade text.

Let's look at the first physical science strand according to California:

MS-PS1 Matter and its Interactions

This appears in both the sixth and eighth grade. Of course, you could argue that those units are all about earth science -- but then that just goes to show that there's a fine line between earth and physical science that's marked only because the topics are taught two years apart (in California).

And the next physical science strand is:

MS-PS2 Motion and Stability: Forces and Interactions

And this is clearly found in all three grade texts because this is covered with the first project of the year (the race cars) in the opening unit, Tools for Learning (which is identical in all three texts).

So it's evident that the Illinois State text is using an integrated model. Keep in mind that we've been using "integrated" to refer to both integration

*within*a subject (Algebra/Geometry, Earth/Physical Science) as well as integration

*between*subjects (Math/Science). Integration in one respect doesn't entail integration in the other -- though clearly the Illinois State text is both. (Then again, we should not be surprised that the

*Illinois*State text doesn't follow the old

*California*traditional pathway.)

I've said before that Integrated Math I teachers would do well to follow my Common Core Math 8 class here on the blog, even though they might be annoyed by the science projects that don't necessarily correspond to freshman year science.

**Examples of New Science Standards**

**So far, I keep talking about the new NGSS, but I have yet to post any actual standards. Well, let's look at some of the standards under this physical science strand, Forces and Interactions. All of these are included in the eighth grade standards (both traditional and integrated models):**

*MS Forces and Interactions*

*MS Forces and Interactions Students who demonstrate understanding can:*

*MS-PS2-1. Apply Newton’s Third Law to design a solution to a problem involving the motion of two colliding objects.* [Clarification Statement: Examples of practical problems could include the impact of collisions between two cars, between a car and stationary objects, and between a meteor and a space vehicle.] [Assessment Boundary: Assessment is limited to vertical or horizontal interactions in one dimension.]*

*MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object. [Clarification Statement: Emphasis is on balanced (Newton’s First Law) and unbalanced forces in a system, qualitative comparisons of forces, mass and changes in motion (Newton’s Second Law), frame of reference, and specification of units.] [Assessment Boundary: Assessment is limited to forces and changes in motion in one-dimension in an inertial reference frame and to change in one variable at a time. Assessment does not include the use of trigonometry.]*

*MS-PS2-3. Ask questions about data to determine the factors that affect the strength of electric and magnetic forces. [Clarification Statement: Examples of devices that use electric and magnetic forces could include electromagnets, electric motors, or generators. Examples of data could include the effect of the number of turns of wire on the strength of an electromagnet, or the effect of increasing the number or strength of magnets on the speed of an electric motor.] [Assessment Boundary: Assessment about questions that require quantitative answers is limited to proportional reasoning and algebraic thinking.]*

*MS-PS2-4. Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects. [Clarification Statement: Examples of evidence for arguments could include data generated from simulations or digital tools; and charts displaying mass, strength of interaction, distance from the Sun, and orbital periods of objects within the solar system.] [Assessment Boundary: Assessment does not include Newton’s Law of Gravitation or Kepler’s Laws.]*

*MS-PS2-5. Conduct an investigation and evaluate the experimental design to provide evidence that fields exist between objects exerting forces on each other even though the objects are not in contact. [Clarification Statement: Examples of this phenomenon could include the interactions of magnets, electrically-charged strips of tape, and electrically-charged pith balls. Examples of investigations could include first-hand experiences or simulations.] [Assessment Boundary: Assessment is limited to electric and magnetic fields, and is limited to qualitative evidence for the existence of fields.]*

I admit that this is a bit more advanced than the class I had back when I was an eighth-grader. Even though eighth grade was always devoted to physical science, the exact content of the class was often fuzzy until the introduction of the California Science Standards (by which point I was already past the eighth grade) and later on, the NGSS.

I've discussed many of these ideas as we read Morris Kline's book in the spring. Indeed, I pointed out that I might read the first few chapters of Kline in my classes.

**Another Bill Comment**

**Earlier today, the traditionalist Bill commented in another thread, this time about free college:**

http://www.cnn.com/2016/08/03/opinions/free-college-opinion-freeland/index.html

http://www.joannejacobs.com/2016/08/cheap-college-is-better-than-free/

Here Bill is replying to another poster, Rob, so let's give the latter's comment first.

Rob says:

I was agreeing up to the point of the “coding bootcamps”. I suppose you can turn someone into a basic web monkey in a few intensive weeks, but you can’t turn out a journeyman coder in that time. This is a distraction, however.

College isn’t for everyone, because not everyone wants a cerebral job (like coding). Lots of people prefer working with their hands and have a job that just ends at quitting time.

In response to Rob, Bill says:

I would agree with Rob, as being able to write decent software (which isn’t web pages, btw) requires a lot of training and skill which a 8-12 week boot camp isn’t going to cut it at all.

Writing secure software is a very difficult task, as I probably found more than 1000 bugs which are actual software errors across 40 or so software programs (some of which support critical internet functions, btw), and correcting those errors can be very time consuming and frustrating.

Coding Bootcamps seem to be the snake oil of certification bootcamps in the early 2000’s, where anyone could simply book study the material and pass the examinations, without ever having touched a physical piece of equipment.

In STEM fields, real learning takes a great deal of time and patience, and not everyone can handle the required amount of coursework…

**There are two issues here -- the first is, do all students need to go to college? Here Rob and Bill agree that the answer is no -- the solution isn't free college or cheap college, but**

*no college*for students who don't need it.

The other is that if students really want a STEM jobs, Bill suggests that such students prepare themselves for the required coursework -- and that begins in middle school, by getting A's in their math and science classes and remembering the material long after the class is over.

**Fractions Yet Again!**

**Let's get back to math, since math is not going away. Yesterday, the traditionalist Bill posted in a thread at the Joanne Jacobs website. As usual, I link first to the article, and then the Jacobs website where Bill commented:**

http://www.chalkbeat.org/posts/ny/2016/07/29/how-do-you-get-students-fired-up-about-fractions-reinvent-math-class/

http://www.joannejacobs.com/2016/08/teachers-study-how-to-teach-fractions/

Actually, let's look at a comment written by another poster, Tressa.

Tressa says:

I suppose it isn’t revolutionary, but I have found that when I talk to people about math, especially those who say they were never good at it, they always were lost when the school taught fractions. Unfortunately, they tell me that they never caught up again.

I am not sure what it is. Do the schools rush through fractions? Do the kids get lost, but the schools keep going? Higher math is, to put it mildly, frustrating if you don’t have a solid grasp on fractions.

So while this probably isn’t rocket science, I will take it as good news that they understand fractions are important and their current method of instruction is lacking. I also think understanding fractions is a developmental issue. Some kids will grasp it later than others, but by that time the class has moved on. The whole thing frustrates me. It is one of the main reasons why I chose to homeschool my kids.

In response to Tressa, Bill says:

Teaching fractions isn’t all that hard…the old plastic pizza/pie/cake usually did the trick in my day, though without a solid knowledge of fractions, a student will probably not master algebra and will never complete algebra II/trig (unless it’s so watered down that they don’t do fractions in that class anymore).

SIGH

Of course, we all know too well what Tressa is saying here. More often than not, the first topic with which students struggle in math is fractions. Tressa writes that her solution to the fraction problem is to homeschool, so that she can tailor her fraction instruction to the pace at which each of her children individually understands. But not everyone homeschools, and it's impossible to provide such 1-on-1 instruction to every student in a classroom.

Bill responds by claiming that teaching fractions is easy. Yet if teaching it were so easy -- why do so many students struggle with fractions? And kids had trouble with fractions well before Common Core, so we can't blame it on the new standards.

Bill continues his post by saying that he learned fractions by modelling them with pizza. But this reminds me of what Dr. Hung-Hsi Wu -- whom I mentioned in my Pi Approximation Post -- says about fractions:

https://math.berkeley.edu/~wu/Schoolmathematics1.pdf

Wu:

*If a fraction is just a piece of pizza, then how to multiply two pieces of pizza?*

Later on in the same document, he writes:

*For example, a teacher familiar with a logical development of fractions would recognize the futility of relying exclusively on cutting pizzas in order to teach fractions. Such a teacher would be more likely to introduce the number line as early as possible.*

*But note the importance in this context of having precise definitions of both 3/8, a fraction, and 0.375, a decimal, as numbers. Anything less (such as only knowing a fraction as a piece of pizza) and this equality wouldn’t even make sense.*

*So we see that Wu definitely disagrees with Bill's approach.*

By the way, notice what's in the article itself:

*But when Kris got to the board, his understanding seemed to vanish. He was supposed to be placing the fraction five-thirds on a number line, but instead he marked off five and one-third, almost four points too far.*

For his part, Cipparone never pointed out Kris’ error that morning. He threw the question back to the class for a quick debate. And even though some students argued their classmate was wrong, Cipparone stood back and facilitated.

For his part, Cipparone never pointed out Kris’ error that morning. He threw the question back to the class for a quick debate. And even though some students argued their classmate was wrong, Cipparone stood back and facilitated.

Now this sounds

*eerily*similar to something posted by Fawn Nguyen, a fellow California middle school math teacher (whom I quoted a few months ago here on the blog):

http://fawnnguyen.com/wbt/

*Mrs. Quiggle: Timmy, where on the number line is four-fifths?*

*Timmy: Ummm. Between four and five?*

*Entire [...] Class: It’s cool!*

*T: Yeah? It’s cool? I got it right?*

*Mrs. Q: Oh, four-fifths is right here. Right about here. If you can just imagine this space spliced up… Yes, that’s right, it’d be sitting right here, Timmy.*

*T: So I did not get it right.*

*[Entire Class -- dw]: It’s cool that you said four-fifths is between four and five, Timmy. We wanted you to be merry.*

*satire*-- a commentary on how strange some progressive teaching methods are. And yet the Live Science link above described a math class that taught fractions using almost exactly the method Nguyen considers to be too satirical to be real -- a student gives an incorrect answer, and the teacher would rather start a class discussion than directly tell the student that he's wrong! (This is often referred to as Poe's Law -- it's often difficult to distinguish between a parody of an extreme view and the real thing!)

As usual, I like to take the middle path between Bill's traditionalism and Quiggle's progressivism. I point out that a traditionalist would have emphatically told Kris and Timmy that they were wrong -- and the students might have resented being told that they were wrong. Traditionalists assume that the students would just meekly accepted that they were wrong, even though it's human nature to defend oneself instead of admitting the truth.

I admit that there is a fine balance here -- how to get a student to accept that he is wrong without wanting to resent it. According to the article, Kris does have

*some*understanding of fractions, so it might be preferable to ask Kris to locate 1/3, 2/3, and 3/3 on the number line, or even to have him convert 5/3 to a mixed number before locating it on the number line -- and meanwhile, that class discussion can still take place. This way, Kris can see for himself that he is wrong -- he is neither led to believe that his answer is "cool," nor does he resent being corrected by the teacher.

Here's another example:

Teacher: What's 2+2?

Student: Five.

Teacher: Hmmmm -- when you add 2+1, you get three, right?

Student: Yes.

Teacher: And if you add another 1 to that, you get four, right?

Student: Yes.

Teacher: So when you add 2 things to 2, what's the answer?

Student: Oh, it's four. (Holding up fingers throughout the conversation would help!)

**Fractions in the Illinois State Text**

The big question, of course, is how will

*I*teach fractions in my classroom? Recall that most fraction instruction occurs in Grades 5-7 (and the article linked above focused on fifth grade), so again, this is not directly related to the eighth grade class that I plan on posting here on the blog.

A big sixth grade topic is fraction division. In the sixth grade module "Playing the Nails," there is an example of the division 3/4 divided by 1/2 using number lines. There's a very similar example of this, dividing 5/6 by 3/4, right on Fawn Nguyen's site:

http://fawnnguyen.com/dividing-fractions/

And so my fraction lessons will be a combination of ideas -- number lines, some class discussion, activating prior knowledge -- possibly even some

*pizza*models, if the students happen to understand these best, as Bill once did.

My next post will be early next week.

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