Depth or Breadth?

So one “problem” that the common core CLAIMS to fix is the idea of a curriculum that is “an inch deep but a mile wide.” Supposedly, the Common Core narrows the focus, which is supposed to allow us to delve more deeply into the concepts presented, so students can master them, develop a conceptual understanding, and hopefully retain a fluency in them for longer.

Unfortunately, I don’t think we truly narrow the curriculum sufficiently – though we certainly are expected to delve much deeper into the topics! So now, instead of being a mile wide, let’s say we’ve narrowed it to half a mile – but we’re now expected to delve a mile deep into the river! So we’ve actually increased the amount of skills that our students are supposed to master, they’re just more connected.

Take for example, my current unit on solving equations and systems of equations. These two topics build well together, but we’re supposed to be moving into systems very soon, and unfortunately, I don’t think my students have mastered solving equations with fractions and decimals – which is the EXPECTATION according to the questions they’ve been asking on the state exam the last few years.

I’m already in crunch time – our first unit lasted about two or three weeks longer than it should have (and the unit exam shows me that that students did not fully master those standards either – no one earned a 100%, and the average from my three classes was 66%). So now I have to make a decision:

Option 1: I spend ANOTHER week working on solving equations with fractions and decimals, and making sure my students are equipped to handle the complex equations (which right now, I don’t think ANY of them are – even my stronger students were a little bit stumped when they saw the one from last year’s exam!). Unfortunately, if I do this, it means that this unit will run at least 1 week too long, and we’ll miss out on time to do another unit… It means I may have to choose which standards I won’t have time to teach at all!

Option 2: I skip ahead to the next topic, so I can “cover” all the units, and I pretend that I’m going to revisit this topic later, but never actually make it back to this skill. I’ll need to choose which standards I think are most important to spend a lot of time on still, but it also means I will need to say “I don’t think my kids can get this and it’s not worth spending time on it.” Even though that’s NOT what I believe!

I think when you look at the number of topics in a year, you really need to consider how much time it takes to MASTER a topic so that students REALLY have a deep and meaningful understanding that WON’T dissipate after a year – skills they’ll really retain for future years. If I could trim the standards for 8th grade, here’s what I would do to make it more manageable:

1. Focus almost entirely on linear relationships and systems of linear equations and solving equations. Each of those would become their own units (these are the functions standards and the Equations and Expressions 5 – 8 standards). I would say dedicate about two thirds of the year to this.

2. I would keep the idea of a line of fit and scatter plots with “approximately linear” data, but I would cut the categorical data representation of “two way tables”. I would throw in this idea of line of fit at the end of linear relationships, after looking at systems maybe (like this year), but I would keep it super short. We would spend about 1/6th of the year on this topic. This is like 3/4 of the current Statistics and Probability standards (not that there’s currently any probability in them!).

3. I would keep the transformations unit, with an emphasis on similar and congruent figures. We would spend about 1/4 of the year on this topic. I might consider including part of the angle relationships with the emphasis on symmetry and understanding that the angles are congruent in certain transformations, but I might de-emphasize this portion as its own unit. This is the

I would eliminate ALL OF THE OTHER STANDARDS. I wouldn’t include circular volume at all (which is currently an “additional” standard, but actually requires a significant amount of time to get students proficient with), I wouldn’t include scientific notation or exponent rules at all, and I would probably cut out the Pythagorean Theorem and right triangles and irrational numbers.

That would give us one set of very related topics (i.e. linear equations & systems and scatter plots with lines of fit) and one geometry set of topics (transformations) that could also be applied to linear equations (though we don’t currently think of it that way). That’s it. None of the this other stuff! Then I could REALLY give my students a deep conceptual understanding of slope, y-intercept, intersection points, etc.