# Teaching Numeracy, Components 1, 2, & 3

Now that we’ve learned the 9 habits, let’s move on to the components of a numeracy-based mathematics lesson.

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If you’re just joining us, we’re reading and discussingย Teaching Numeracy, 9 Critical Habits to Ignite Mathematical Thinking, byย Margie Pearse and K. M. Walton.

### Critical Habits 1, 2, & 3: Purpose and Focus, Ignition, and Bridge to the Learning

“Psychological research suggests that learning is a constructive process. It entails making connections, relating new knowledge to what is already known, and applying knowledge to new contexts.”

I will apologize in advance for a short post this week, and I trust you all will pick up my slack. I flew into Virginia today (Sunday) for a workshop I’m presenting, but my luggage did not fly with me! In just a few minutes, I’m heading to the airport to see if it came in on the 11:55 PM flight.

I really like how the authors now begin to weave all of the habits together into a blueprint for effective mathematics planning. This, of course, begins with understanding your purpose for the lesson. As they point out, this is not about what you want the students to be able to do, but what you want them to understand. In other words, the deeper connections and understandings. The ignite component reminds me of the engage step of the 5E model, which is very popular for math and science in our district. It’s that hook to get the students interested in the lesson, which is critical. But I also like how the authors mention the importance of having a structure in the mathematics classroom that “creates a culture of rigor and an atmosphere of deep thinking.” (p 131)

The bridge activities that I liked the best were Three Facts and a Fib (p 143), Discovery Through Manipulatives (p 144), and Examples and Nonexamples (p 144). ย I’ve used Three Facts and a Fib as an ice breakerย activity–three personal facts and one fib–but I love the idea of applying it to content learning.

I told you it was going to be short! ย Wish me luck on the luggage…

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1. Margie Pearse says:

Gosh, Donna, I am hoping you and your luggage have reunited by now. I am sending good thoughts and prayers your way.

I have found the Bridge to be the most powerful tool for providing equal access to the learning to come. It goes deeper than an “anticipatory set” by frontloading just enough for all student to enter the learning in some way.

I am a believer in students sharing background knowledge. The conversations that naturally come up during the Bridge provide the necessary entryway into the learning for everyone.

My favorite Bridges are “Give-One-Get-One,” “Examples/Non-examples (then have groups generate a definition from this), Discovery through manipulatives and problem situations (followed by a Chalkboard Splash with students noticing similarities and differences in various group strategies), Line-ups, Three Facts and a Fib, and Mix and Match.

1. Donna Boucher says:

My luggage and I were indeed reunited at about midnight! Your emphasis on background knowledge has given me a new appreciation for the value of building those connections.

2. TheElementary MathManiac says:

This book keeps going back to the big idea of math not being about kids just doing it but rather than understanding it. So many great ideas! I left my copy at home and am on vacation but will be back with more comments next week!

Tara
The Math Maniac

1. Donna Boucher says:

Exactly, Tara. Understanding is what makes math a thing of beauty. Rote memorization holds no fascination for most students.

3. Ellen Barnes says:

I love the quote that starts off component 2! Einstein loved learning and I believe the best gift we can give children is education. I was intrigued by the research that states that students will retain 70 percent of the information that they received in the first 10 minutes of class and only about 20 percent of the last 10 minutes. Really something to consider when planning your lessons. Setting a focus and planning ignition activities provide review and number sense will be a focus of our next PD.

The bridging activities were great because of the power they hold to engage the student. I love the reference to Newton’s First Low on Inertia: A student at rest stays at rest unless acted upon by an outside force. This made me smile! I want interest in the eyes of my students. I would have the students use their math notebooks for the bridging activities whenever possible. My favorite ones were word toss, greet and go, and three facts and a fib. I really liked the T.H.I.E.V.E.S. strategy for use with any subject area. We are really pushing the concept of “Look for the Evidence”, so I plan to introduce this strategy to the staff.

1. Donna Boucher says:

Yes, Ellen! That piece of research about retention was very eye-opening!

4. Sandy says:

I think the Ignition piece is so important and well worth the time. The emphasis is on real thinking and justifying your thinking. It allows the teacher to quickly determine which students are making different types of connections. I, too, was intrigued by the idea that students retain so much more in the first few minutes of a lesson and will challenge myself this year to create thoughtful, purposeful beginnings to my lessons. I usually only have 30 minutes with my small groups for intervention, so this will be a challenge! My favorite bridge activity is definitely “discovery through manipulatives”. This would allow me to quickly see where each student is entering the concept and to differentiate quickly.

I hope you found your luggage Donna!

1. Donna Boucher says:

I’m with you, Sandy, thinking about how to best incorporate these ideas into a 30 minute intervention block.

5. Sandy says:

Hi Donna,
Not related to the book but ….any chance you will be presenting at the NCTM Boston conference in April 2015?

1. Donna Boucher says:

No, sorry, Sandy. April is right before our state testing, and in my new position I wouldn’t feel right being away during that time.