Tyler,
This I understand. I am a JK-12 Math Chair and have meetings with teachers at all levels. I would say that even the “best trained” math teacher at any level, has trouble in connections. Knowing math is not the same as understanding and being able to teach it. We use Investigations, which is a very detailed course and flow. Teachers who spend the time reading it, following it and teaching – often find the inquiry is there, they can lead a good conversation and like math.

So not my to answer the question – I think the ONLY way to bridge a divide – is to have “flow”. This means a consistent “text” and series flow JK-12. The issue here is everyone wants to add their own “spices.” And some schools are way too big. We have 1000 students JK-12 and for the most part, there is a flow. The divide is because we operate in “silos” and as “islands” (by schools, by subjects, by grades)

I would say that what I generally see in Elementary school – using manipulatives, activities, etc… is essential.. it should “last all the way to grade 12 and beyond”. So it does work in both directions. I actually see “new” ideas about HS teaching and wonder – because I saw in in the earlier grades. If you can – observe HS and MS teachers – but NEVER i mean NEVER – think “I need to prepare them for that teacher or that challenge”…

only think – I need to prepare my kids to think and adapt.

Joe and Dan,

Apologies, I should have better clarified the word ‘divide’ better. I haven’t checked back past few days. Flu got the better of me.

When I say divide, I think I mostly mean in terms of instruction. I’m in elementary and am about to make a wide sweeping generalization (so forgiveness if it’s too big). I think many of us, not all, in elementary, if we’re being honest, do not understand math to the level we should. We don’t always understand how early childhood to elementary to adolescence to high school builds mathematically.

I think our instruction really matters, but I couldn’t tell you specifically how it builds for later mathematical development. Likewise, I couldn’t do what you do in the classroom. I could run a lesson, but I couldn’t interact with the math. Just being honest. But I think our elementary instruction could become more robust if we could. I’m not sure if it works in the opposite direction? HS to elementary?

So my question was asking how we begin to bridge that divide? Hope that makes a bit more sense.

The challenge I’ve had is anticipating how students will approach a task and misconceptions they’ll have (which are sometimes about life and not about math), and planning my responses to their struggle so that it stays productive.

Right! Our most interesting struggle was around the different jar question. The math was more straightforward. That was interesting.

Thanks for sharing, Lisa. I had to call out one of your paragraphs with a “whoa” above. I hadn’t given enough thought to the difference between students whose entire education was in the Common Core era versus those who have had to adapt. Very provocative. Looking forward to checking in on these ideas more at CSUEB later this semester.

There seems a divide, sometimes unhealthy, btwn the world’s of ET and HS (understanding, bias, instruction, content, etc). Thoughts on bridging that divide?

Great question. There are certain tasks, like the Pool Border problem, that have hooks down in primary instruction and can extend up to secondary. I wonder if lesson studies ever cross that many grades.

100% yes

So far this year I’ve taught in 1st, 2nd, 4th, 5th and 6th grade classrooms, sometimes using the same task with different grade levels which has been very interesting to see how students see and approach things differently. It’s been a great learning experience.

whoa

Nevertheless, I could have an exaggerated perception about these generalizations, but the distinctions are, at the very least, quantifiable.

I was enthralled to read in your post that these fourth-grade students seem to have a firm grasp on number sense, and that you didn’t notice anyone “carrying” digits during the multiplication process. I feel like if I had had this exposure and opportunity when I was in the fourth grade, I would feel more confident teaching at the elementary-school level. The new standards are a filter, in a way, to ensure that teachers actually *understand* mathematical concepts, instead of simply teaching procedures. It wasn’t until I started university that I began to fully comprehend the “why”s and “how”s of mathematical mechanics. In fact, I found myself guilty of using a procedure when investigating Graham Fletcher’s 3-Act Task. In the first video, I made an estimate of the number of Skittles in the jar. But then in the second video, I used the information provided about the number of Skittles in each bag, and the number of bags used, to adjust my estimate. How did I do this? I took the product of 14 (the number of Skittles in a bag) and 58 (the number of bags). Yes, I fell for this trick! It took a moment to realize that the number of bags was fixed, but the number of candies within each bag is likely to differ. It’s these conceptual habits that should be fostered within students, beginning at the youngest possible age. I believe that children are naturally curious about these activities as it is, and already have an inherent sense of wonderment. But somewhere along the way (before the new standards), this desire to learn was hampered by robot-like procedures. These children are the future, and I feel very inspired knowing that they seem to be on an optimal path!

What do you mean ‘divide’?

perplexing!

I featured a bit here I thought was really helpful. Your comment helped me realize that my aesthetic preference for secondary math may result in part from a wobbly understanding of primary math.