Those doing the most thinking are doing the most learning

I am taking baby steps towards converting to a math workshop model with the help from reading Minds on Mathematics. There is much more to the model than breaking the class time into chunks:  1) roughly 10% of class time on an opening task, 2) 20% devoted to the mini lesson, 3) 50% work time in which the teacher confers with the students, and 4) 20% sharing and reflection. It’s about creating a culture of learning, where students…

engage with worthy, minds-on tasks and important mathematical ideas; enjoy time to think, work, and communicate; construct mathematical understanding for themselves; and notice their own development as mathematicians.

A lot of planning and preparation goes into this approach, but once class begins those doing the most thinking are doing the most learning. Over break I’ve been doing a lot of thinking about my “practice” and I have learned that I am not pleased with myself. In terms of planning and preparation to create this culture of learning, I’d rate myself as mediocre–which is a scoch to the right of basic on the Danielson model.

I’d be fool to say I’m going to fully implement a workshop model as a New Year’s resolution but there are some measures I can take along the way.  Originally I thought the “right” thing to do would be to commit to one change then slowly implement another. For example if I don’t like the way I begin class (which I don’t) I’ll work on the opening task. But since the opening task leads into the mini-lesson, which leads into work time, etc. I need to rethink the entire class period for that day.

Wendy Ward Hoffer, the author of Minds on Mathematics, suggests an opening task be: a new problem, a problem from previous homework, recent class work, or a concept central to the unit of study. The task should also be a springboard into that day’s lesson and it should have multiple entry points so all students have access to the problem.

When we return from break the seventh graders will be multiplying and dividing fractions. Based on their pre-assessment they don’t have a deep understanding of the concepts. So I’m working on a series of brief, scaffolded tasks that will lead into two mini-lessons.

multiplying fractions1

The recipe problem is heavily scaffolded, suggesting repeated addition as a visual representation, and using multiplication to represent the problem. At this point I’ll conduct a skinny, mini lesson on multiplying fractions by whole numbers.

The next problem is less scaffolded.

multiplying fractions2

At this point the lasagna problem will launch a mini-lesson on multiplying fractions by fractions. I created a video for students who will be absent.

Plus the students will have this handout  to take notes during the mini-lesson. I’ll do some white board work to check for understanding the visual model. Now here’s where I’ve  run out of gas for the time being. I need to find or create some differentiated resources to use following the mini lesson. Some students will catch on immediately and I may want them to explore simplifying fractions by examining their common factors:

factors and simplifying

For students who struggle, I’ll need to have at the ready some additional visual model problems for in class practice.

Additionally, I may have the students work on this MARS yogurt problem while I’m conferring.

Sharing and reflection will be students presenting a variety of problems they’ve been working on during their work time.

I’ve spent hours thinking about this ONE lesson and I’m still not fully prepared. The sheer fact of thinking about it however will make it a thousand times better.

Next up will be dividing fractions by a whole number then dividing fractions by fractions. I haven’t sketched out the whole number mini lesson yet, but here’s the direction I’m headed with dividing fractions by fractions.

Dividing fractions by fractions

I know I’m getting ahead of myself but the dividing fractions by fractions lesson will look similarly. I haven’t yet created a video or handout but it will be based on these problems.

dividing fractions1

I’m troubled by section 4. It’s too scaffolded and not enough discovery. I need to work on that. Suggestions???

dividing fractions2

Again, I’m troubled by section 4.

The visual models you see in this post are based on a handout I found while scouring the internet. I liked the overall idea, but tweaked it to be a bit less paint by numbers. This is still a work in progress.


3 thoughts on “Those doing the most thinking are doing the most learning

  1. I’m really excited to see you dipping your toes into math workshop. I have been doing math workshop in my classroom this year. It is really a shift in instruction. I use Carnegie Learning as my math curriculum which really lends itself to rich problems.

    I love the opening. We do a warm-up everyday. That’s also when I stamp HW for completion and students self correct using the answers projected from the Elmo.

    I also love the mini-lesson component. Many days it’s really tough to stick with a 10 min max lesson. I go over some days, but not most.

    The work time is when the students really dig in and do the math in their collaborative groups. They impress me with what they accomplish.

    The sharing/reflection is so important and yet sometimes I just run out of time and have to hold it over for the following day.

    I am STILL struggling with the conferring aspect of the workshop model. It continues to be my achilles heel.

    I really need to start blogging again about how math workshop has been going. There have been so many amazing things going on in my classroom, but there is definitely tons of room for improvement.

    Good luck on your workshop journey. It is totally worth it. I can’t wait to hear about how it works for you. I’ll see if we can get our twitter chat on Minds on Math going again in 2014.

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