Reflecting on Habit 7 Summarize, Determine Importance, Synthesize

The authors of Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking begin the chapter on Habit 7 with this sentence, "Determining importance, summarizing, and synthesizing are related acts that together comprise one of the most crucial of the nine critical thinking habits."

In the chapter they talk about note-taking and journaling. This past year I encouraged students to use the Cornell Note System.  I created the structure for them; and for some students that worked well. Others struggled with notes.  They were good about class discussion, working out examples, but taking notes seemed to be a challenge.  I've been thinking about how to improve note-taking in the coming year.

I especially want to take more time with summarizing the lesson.  I know how important it is in my own learning to stop and reflect for a moment on what I've learned and how it connects to previous thoughts.  Stop and jot is a tool - helpful for summarizing learning as is One Minute Write.  Another tool is creating study cards.  I did not use this at all last year, but in the last few months I have seen examples of sketch noting that would make awesome study cards. And study cards would be good tools for interleaving practice.

My take-away from this habit is that I need to allow more time for reflection.  Summarizing can't happen well if we are frantically working right up until the bell rings.  My goal ... set my internal teaching clock to allow reflection in the last five minutes!

An aside about journaling ... it's a great tool as well.  My students blog but I don't require a particular topic.  So some students use their blog to synthesize learning.  Others use it to curate interesting ideas they are researching in math.  I want to continue student blogs in the coming year and I'm trying to decide what purpose is best.

NoteTaking - why Cornell Notes?

I love the "BLAugust Challenge!" So I'm going to jump in this month to share a few things I found helpful in the classroom, some favorite sites and tools and such!

Today's blog is inspired by @MarshFosh73's tweet today ... she wrote:
Input needed: How do you give notes in class? Do you give your students typed, fill in the blank type notes? (This is what I do, but am 2nd-guessing.) Do students write notes by hand? Do students take notes on a device? #MTBoS #geomchat

I have created guided notes ... and my colleague next door still does.  But in my last year or two, I tried to go to a more open Cornell Notes style.  Our school emphasized using Cornell Notes across all disciplines.  Some teachers provided the guided notes in that format.  Personally, I like my note-taking to have more flexibility.  So in the first weeks of school I shared various graphics of Cornell Notes, explained why they were important, provided some structured time to set them up, and to complete them.  We even shared a time or two what each of us wrote in our notes ... so that we could get some feedback.

Basically Cornell notes have 3 areas ... cues/questions on the left, notes in the larger right column, and a summary at the bottom.  One routine homework assignment was to create appropriate cue/questions on the left to go with their notes, as well as to summarize the day's work.

I am curious how other folks organize their notes for students in upper levels of math!  How much structure do students need?  

If you want to participate in Mrs. F's twitter convo ... here's the link!  Share your note-taking style!
#BLAugustChallenge2018

#70Days Lesson planning - Cornell Notes

Writing about the things I haven't done yet this summer was motivating.  Today I worked on lesson plans for our unit on systems of equations.  I plan to use Cornell Notes to guide instruction so I focused my energy on those.  I also found/adapted problem solving for each of the four lessons - solve by graphing, substitution, elimination, and systems of inequalities.

Here are the Cornell outlines for each day:

Day 1 Solving Systems of Equations by Graphing

Day 2 Solving Systems of Equations Using Substitution

Day 3 Solving Systems Using Elimination

Day 4 Solving Systems of Inequalities

For my units I am creating 4 documents: a warm-up, a set of notes, a group problem to solve, and a homework set.  I'm feeling pretty good about the first two units.  They still need polishing ... but getting closer!  Hopefully with this basic planning done, I can spend some quality time on daily assessments - short, efficient - with time to write meaningful feedback!

#70Days Systems of Inequalities Lesson Planning

A bit of lesson planning tonight ... still thinking about systems.

This year I want to organize our notes using the Cornell formatting.  In the first unit the notes are scripted with fill in the blank.  In this second unit, I've included the focus questions and will guide students in taking notes in the main section.

Students will start in small groups.  They will discuss the guiding questions and make notes on whiteboards.  Then we will reconvene as a whole class to discuss together, compile their thoughts, and make notes.  Whole class discussion is described here.

After discussing the notes, students will meet again in their groups to work through the given problem. Students will create posters of their work to display.  As students are working, I want to try a formative assessment strategy entitled, "What are you doing and why?"  It's #73 in the book, Mathematics Formative Assessment: 75 Practical Strategies for Linking Assessment, Instruction, and Learning.  After students have had time to get well into the problem, I will ask them to "press pause" and respond to the question, "What are you doing right now? and "Why?"  Students will have just a minute or so to explain what processes they are doing and why.  I hope that in using this particular strategy students will become more aware of their thinking and have the opportunity to hear the thinking from other table groups.

We'll hang the posters and share the outcomes.  At this time we will discuss how the polygon formed by intersecting inequalities informs decision making in a linear programming problem.

Here is a copy of our notes:

Solving Systems of Inequalities

#Made4Math: Cornell Notes ... work in progress

I struggle with note taking ... and note giving.  When I was in school, I had a particularly good memory.  If I listened in class, I rarely needed to write anything down.  And my notes were haphazard at best.

In my teaching I realize that I don't like routines ... I like for each day to be a bit different than the day before ... so giving notes usually looks somewhat different.  And I often prefer a discovery type lesson so I don't give notes per se.

But I realize that some students would benefit from learning how to take notes and from a consistent pattern to those notes.  I've been thinking about learning preferences this week and I want to do all I can to meet the needs of my students.

So I'm thinking about writing out my teaching notes in a specific format ... using Cornell style notes.  And I want to teach students how to use this format as well.

With that in mind I've written out notes for the first few class days in our first unit on the foundation of functions.  I'm sharing these "notes" as my #made4math submission.  I would love your feedback.

Cornell Notes Folder  (You have to download to see the notes in the correct formatting)

Already one team member has asked why the "fill in the blank" mode - seems so scripted.  I chose this model for the first unit to help students with structure.  I also wanted them to have a clear basis of information about functions before we jumped into the rest of the units!

In the next unit I want to use sentence stems.  In the third unit, maybe just provide questions.  In the fourth unit students might be on their own with some guidance from me as needed.

Even while I post this particular note, I am conflicted about interactive notebooking.  It looks like so much fun ... and yet it also looks like it takes so much time.  Your thoughts?

One more caveat ... I would not start the lesson by reading and filling in the blanks to these notes.  We will start with an activity on each day and then go to the notes and discuss the words.