*Edited to clarify: This post is not about the IB but about the Dutch national curriculum*

This year I teach almost all of my classes within the International Baccalaureate (IB), so I have only two classes within the regular Dutch curriculum, one 7th and one 8th grade. These are students who have decided to take their schooling bilingually (though the majority of them are fully Dutch and have never spoken [much] English before). They begin in 7th grade directly with half of their classes, including math, in English. That’s a pretty daunting feat and these kids are all very bright. Yet I feel discouraged and sometimes even dread these classes.

Why? It starts with this tweet from David Wees:

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```A textbook is not a daily lesson plan.

— David Wees (@davidwees) September 5, 2014

That’s an image of the “study planner” that I need to follow for this term. It was made by a colleague, and if I don’t follow it then we end up out of sync and it becomes unfair for the tests, not to mention I don’t get through the material that the students “need to know for the next year.”

We have just two lessons (of 75 minutes each) per week with the students for an 8-week term, but are constantly losing days from our schedule by things like a day off from school, or a test planned during our lesson, etc. So you figure approximately 14 or 15 lessons per term. Times three terms plus one term where we have them only once a week (yes, that is as productive as it sounds), and that means I have to cram 8 chapters worth of material into about 52 lessons.

And honestly sometimes the curriculum careens wildly around. In the first “real” lesson I was meant to do:

1.1 Theory A: Using Letters (Writing Expressions) 1.1 Theory B: Addition and Multiplication using Letters 1.2 Theory A: Multiplying out brackets (Distributive Property)

Just to give a quick example of what sort of problems the students are expected to do in one lesson, it veers from:

“Tessa earns

beuros per month. Her sister Sandra earns three times as much. How much does Sandra earn?”

to:

-2p * 3q – 2p * -5 – 3q * -2p – 4p

and finally to:

2/3x(18a – 12b – 3c) – 1/4a(48x + 4b – 8c) – b(c – 8x – a)

What an absolute SWEAT to get through that. *My* brain hurts thinking about it.

So in the second lesson, a full quarter of my class had clean-up duty, which means that they have to sweep the school after lunch (YES THIS IS REAL, I AM NOT JOKING!!!) so they came 15 minutes late to my class. So I took that time to have the rest of the class work together on this worksheet I made for them on writing expressions and combining like terms:

I’m not trying to act like this is the most brilliant worksheet ever, but I think it did serve a purpose, because I saw kids write abcd instead of a+b+c+d, kids who wrote a^2 + b^2 + c^2 + d^2 instead of 2a + 2b + 2c + 2d, kids who wrote a + b + c + d * 2 instead of 2(a + b + c + d), kids who couldn’t come up with 9 – (a + b + c + d) at all and more. So what that says to me is that kids cannot just steamroll through everything. They need recap, revision, and time to reflect. It is helpful for them if I bring in extra things for them to do and let them puzzle through it.

But no matter because in lesson two I was supposed to do:

1.2 Theory B: Multiplying Binomials 1.3 Theory A: The Remarkable Product (a+b)(a-b) 1.3 Theory B: The Remarkable Products (a+b)^2 and (a-b)^2

After “wasting” so much time on the variables on a map thing, I could hardly get through this and ended up assigning the majority of it for homework.

Sure kids, I know you’re only 13 and you’ve *just* learned how to multiply binomials for the first time ten minutes ago, but do you think you could please now do this problem for me: (2a + 3b)^2 – (3a + 2b)^2? Because I really don’t have a lot of time to make sure you understand it and give you cool projects around this like Babylonian Multiplication, because in the next lesson I have to do:

1.4 Theory A: Simplifying Algebraic Fractions 1.4 Theory B: Adding Algebraic Fractions 1.4 Theory C: Multiplying and Dividing Algebraic Fractions 1.5 Theory A: Scientific Notation of large numbers (WOW, how is this related??)1.5 Theory B: Scientific Notation for small numbers

I felt so damn shitty after this lesson (and also my 7th grade lesson, which is even more intense, especially when you consider that these kids are in high school for the first time ever and don’t even speak the damn language of their textbook) and horrified looking at what I have to do in one lesson next week. Basically, what it comes down to for me in these classes is that if I do anything that’s not in the textbook or that takes any serious amount of time for thinking and discussion, I won’t be able to get through the curriculum. I always like to start Scientific Notation with a reading from Bill Bryson but it’s like, AHHH, that will take at least 10 minutes!

I really don’t know what to do about this. I agree with David Wees. I feel like I have to teach in a manner that’s directly counter to what I think good teaching is. So that’s why I’m already discouraged for my Dutch math classes. Any advice?

1. Is it possible to figure out what the big ideas are from this curriculum, and to re-arrange it into units to fit those big ideas? Then it becomes easier to focus on the big ideas and not so much on the minutia. It also becomes easier to figure out what things are critical that are taught, and what things are distractions or extras.

2. Grade 7 seems early, if you are backwards planning from the IB, to be teaching algebraic fractions especially if this is the first time students are learning algebra. What understanding of fractions do your students have? What understanding of variables do these students have? Is it possible to start discussions with other people in your school about this situation? I might find out the answers to these questions as part of my investigation into revising this curriculum.

3. What evidence does your department have that this approach is working for students? It seems clear, based on your account at least, that this does not seem like the best choice that could be made, but maybe, somehow, it is working nonetheless? If it is not working, and you can present evidence to that effect to your colleagues, maybe they will be spurred to take collective action?

4. What did students learn in mathematics the year before? What will they be learning next year? How does this set of “objectives” fall within the scope of these students’ experience in mathematics?

5. It seems clear that the list of things that are listed as objectives are not actually lesson-ready objectives. It might be worth finding some readings on the impact of educational objectives on learning. Doug Lemov, Dylan Wiliam, and pretty much anyone else I have read on the subject, all suggest that learning objectives should be attainable and measurable. Maybe framing these objectives in terms of the types of measurable information you can gather, and then gathering evidence of the students movement toward these objectives (this requires a pre and a post assessment to measure change in the student) would help you gather some evidence for your colleagues as to the ineffectiveness of this type of curricular structure. Or, you will discover that it works and nothing needs to change (I highly doubt this).

These questions are written from the perspective of someone who knows you want to do the best you can for your students, and maybe you are looking for questions you can ask yourself and your colleagues that will get them wondering about the effectiveness of this shared curricular approach.

Hey David, thanks so much for taking the time to write these detailed comments. First I want to clarify that this is

notIB at all. My IB classes are FANTASTIC and well-paced and I have all the freedom and creativity in the world. This is for the Dutch curriculum.The rest of your comments are really helpful and I want to respond to them fully:

1) I had rearranged the curriculum in previous years when I was the coordinator for this class, but now we have new books and someone else is in charge. The new books are basically just the old books but more difficult, haha! I really stand by my rearrangement of the material though and I think I always did my best to ensure that things were logical and built upon each other in a way that helped ease the cognitive load. The kids didn’t like that it skipped around the book, though.

2) These kids are in 8th. They do see it in 7th grade, which I’ll detail below.

3) This is a GREAT question. We are apparently going to be getting a department report card very soon and I was tipped to some interesting knowledge about this. In the Dutch department (I don’t know if this includes the bilingual classes), something like 40% of 8th and 9th graders fail math!!! I think that’s RIDICULOUS. I have never had such high failing numbers. I think that speaks to something systemically being wrong and I can’t wait for this discussion to start!

4) 7th graders get introduced to evaluating letters in formulas in chapter 4 of 7th grade. Then in chapter 6 of 7th grade they do calculations with letters, which includes combining like terms and multiplying, as well as simplifying algebraic fractions (monomials only) and adding algebraic fractions (also monomials only) with like and unlike denominators. Then in chapter 8 they again do combining like terms and multiplying, but adding multiplying out the brackets (distributive), calculating with powers (including the rules for multiplying, dividing, and raising to a power as well as scientific notation). I think that’s quite a lot for 7th graders! So much of this is apparently review for my 8th graders, but I cannot imagine that the 7th graders retain that much of it for 8th grade if I consider that they fly through at the same pace in 7th grade as we are doing in 8th grade!

5) Thank you for the recommendations on these readings. I would like to bring it to my colleagues as well, because the basic way that things work in the Dutch department of our school is that they explain the theory of a section of the textbook, and then the students work on exercises from the textbook. I have to say that our results on the national exams are not high so perhaps I can convince others that this is not the best way to go. YET last year I gave a presentation on the work my IB students did on Dan Meyer’s Taco Cart (which I was so blown away by and proud of) and the biggest reaction to this was that I lost two lesson days on this. Sigh.

Thank you for all your feedback. Again I want to say that my IB classes are nothing like this!!

Sorry, I should clarify that I assumed that these students would eventually end up in the IB diploma programme, and so I also then assumed that part of the point of this curriculum was to backwards plan from what is necessary for students to be successful in that programme.

I hope you manage to open up this conversation with your colleagues.

Ah, no, these students won’t go on to the IB; they’ll take the Dutch National Exams.

We have two schools housed in one building – a regular Dutch high school (which includes a bilingual department) and an IB school (which has MYP and DP). The two schools are entirely separate except for the fact that they share the classrooms and the teachers. It’s a bit of a weird situation but I think it’s good for both parties in a way because the IB students are not isolated from the country that they live in. They are actually in an extremely Dutch environment. The Dutch students for their part get to always hear English being spoken all over the school.

For all of the hype, the IB is a fairly low-level, skills-based curriculum, much like what is taught in non-IB schools, except that it seems to suffer from an overly rigid structure and a breakneck pace, as well as lacking a comprehensive vision. We empathise with your predicament.

Instead of a series of 9 algebra notation exercises built around a scenario, in which students are so busy reading and writing, they don’t have time to focus on the important underlying mathematics, we are inclined towards single tasks that are approachable in myriad ways.

This problem, for example, http://fivetriangles.blogspot.com/2014/02/143-bicycle-ride.html (which can be automatically translated into Dutch), can be solved both arithmetically and algebraically, but it’s when students recognise that algebra can do in a seemingly different way what the arithmetic did that real mathematical enlightenment may occur.

I’m sorry, I think you’ve misunderstood: This is

notmy IB classes. This is the Dutch curriculum. The IB is a wonderful program and it doesn’t have a rigid structure or breakneck pace at all; I also don’t find it low-level or skills-based, at least not the way I teach it! I’m not sure where that idea comes from.The IB does not prescribe curriculum at all in the elementary and middle schools.

The IB diploma programme is definitely not low-level and I think it is definitely possible to teach the IB diploma-level mathematics in a way that leads to strong conceptual understanding, but that it is also possible to teach it as a set of somewhat disconnected skills, and unfortunately both can lead to student success on the end of programme exams.

That we suffer from terminal confusion over indistinguishable-to-us curricula does not alter an unfortunate reality: primary and secondary mathematics is almost universally taught as a series of discrete skills, whether they be “low-level” arithmetic, or “high-level” calculus. Cloaking those skills in “real world”, arguable scenarios (and other modern reform attempts) does not break out of this limitation. What we mean by “low-level” is not the range of content, but the depth of problem solving analysis that is required of students, and its commensurate ramping up. We didn’t mean to pick on IB specifically, but a vision beyond the mere mathematics continues to go absent from most modern curricula.

With this approach (the Dutch one) algebra as the process of pushing symbols around is a game. Yes, it has rules, the rules of arithmetic. The letters are best seen as names for unspecified numbers, and when a number is specified you can replace every occurrence of the name by that number.

Why not let them build their own expressions, and rearrange them.

Here’s a simple one:

Starting with a + b we can write this as a + ab/a and then as a(1 + b/a)

If we let b be a^2+3 then this gives a(1 + (a^2 + 3)/a)

and then a(1 + a + 3/a) and so on.

Substituting values in each step is the essential check.

You can have fun with a^2 + b^2 and a^2 – b^2 this way.

Best of luck with your efforts to enlighten your colleagues.

Whenever I come across a bit of maths in a blog I start thinking!

Here is today’s:

Factorising a^2 – b^2

Set a = b + c

then we get (b + c)^2 – b^2 = b^2 +2bc + c^2 -b^2 = 2bc + c^2

which is c(2b + c) which is c( b + b + c)

Substitute back with c = a – b and get (a + b)(a – b)

I then tried it with a quadratic y = x^2 + bx + c

and did x = z – c

You can finish this one off!