These are my notes from Nanci's presentation this morning. I highly recommend you go to her website and look at her NCTM file. She had an hour and stuck to it and because of the time constraint, there were many things she went through quickly that I don't have great notes on. I would have gladly listened to her for an hour and a half and it would have been even better if NCTM would have let her do the gallery workshop she would have preferred to do.

As math educators, we want math to be

**understandable (clairify the curriculum)

**appropriately challenging

**engaging

The last two can be covered with differentiation.

We need to differentiate in three ways -

**Readiness - want maximum growth with appropriate challenge

**Interest - motivation (all kids have different ones)

**Learning Profile - how do brains function NOT learning styles. This is the most efficient way to teach students - there is no reteach even though it may take no time.

She did mention Understanding by Design which is on my summer list of things to check out.

__Understandable__

Dissect into three parts:

Know - facts, formulas, vocab, "how to"

Understand - big ideas (what makes math math and not arithmetic), concepts, strands through units/grades, mathematics v. arithmetic. These are in sentences in her classroom

Able to Do - skills, transfer, evidence - As a result of knowing and understanding I can...

Closure is important - at minimum have students share with a neighbor how they better understand the big idea of the day and then have a couple share out their discussion.

Understanding math includes but does not mean number crunching. She then went through a development of addition and subtraction from whole numbers all the way through Calculus. The overarching idea she talked about is that you can only add or subtract things that are alike. And if the things are not alike, is there a way to make them alike so you can add or subtract them. Seeing this really hit that home with me.

__Appropriately Challenging__

**is like one size fits all clothing (it doesn't, and not everything we do fits every kid)

**look at the whole picture - the journey is often winding and you need to find the entry point (back to readiness) relative to a particular understanding or skill

The appropriate challenge is 10-15% from where they are when they start. How do you measure that??? The next step from where the student is at is where to begin.

If you only differentiate by readiness - you will be tracking your students (don't want to do that!).

__Readiness__

**students are all over the place

**how do I structure lessons for different entry points?

Nanci then proceeded to put up a slide that had three different color groups (green, red, blue) and a list of activities the group was to be working on to develop their understanding of adding fractions. The assessment or homework activity - not really sure which because she was flying and I was trying to keep up with my notes was also listed. This slide is in her presentation - take a look at it to get the details. The biggest thing I got lost with in here is how to implement it. I've never done anything like this in my classroom. If I have three groups (or more), I can't be with all of them at once. And I don't necessarily want to start with the lowest group first because that might call attention to them and I don't want that either (although I suppose if the classroom culture was welcoming and open, etc. like it's supposed to be when you use rich problems so that students feel welcome to mess up it wouldn't be an issue). How do determine where to be first and get them going, while still being "less helpful?" Still working on figuring that out.

She also talked about using two columns for notes among other ways. Her method was based on Cornell notes and I really liked that she had on the Model side everything spelled out and then left the kids to go on their own on the other column. Still trying to figure out whether to have the paper in front of them like the screen with everything written out for them with hints or to just have it on the smartboard for them to copy. But I liked the idea and will incorporate it.

__Engaging (make it relevant)__

If it's too hard/easy

If I'm not interested

If it makes no sense to my brain - How am I going to be engaged??? Goes back to the readiness, interest and learning profile from earlier.

She had a list of things to help make it engaging which I missed but I did catch that novelty was a great way to engage students. She talked about a couple of games that you can easily create instead of giving students worksheets so they would work through the problems. Check out the NCTM file for details.

She also mentioned Dan Meyer's TED talk and be less helpful. Her comment on it was that you are enabling students when you help them. If we aren't less helpful, kids won't be independent learners. Give them a list of questions to guide them. I felt this directly tied back to the Productive Struggle session from yesterday.

The last major thing she talked about were Learning Profile cards. Learning profile refers to how an individual learns best - most efficiently and effectively. She has a learning profile card on the website as well as some other files that I referenced earlier that are related. Again, I was having trouble keeping up and at this point the session was almost done so she was really flying through stuff. The learning profile cards help to assign students to groups by how they learn. As part of the presentation she listed the top three reasons for using the learning profile cards. The #1 reason was to create a community of learners. Definitely something I want. Her main point with the learning profile cards was "How can I help you best if I teach you all the same way?" Gardner's Multiple Intelligences and Robert Sternberg's Intelligences (which I had not heard of before) are a part of this.

The last few minutes were sharing some activities using differentiation (also part of the slides). I really felt this session was valuable and had a lot for me to think about. This gets added to the summer list for exploration as well.

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