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Archive for CCSS Mathematical Practices

Noticing and Wondering in Middle School

by Suzanne Alejandre
September 15th, 2013

My colleagues recently blogged about Noticing and Wondering in High School (Max – @maxmathforum) and Noticing and Wondering in Elementary School (Annie – @MFAnnie) and as I read both of their blogs, so much of what they write about applies to a middle school classroom. In my experience the biggest bang for your buck in using this strategy is engagement of all students! As I’ve worked in elementary classrooms the feel is a little different from middle school — the younger the students the more I feel I’m tapping into enthusiasm that hasn’t been dampened yet. As I work with fifth grade or sixth or seventh or eighth graders I often feel that there are more years of disappointment and/or disillusionment that have to be countered.

Middle school teachers (and, of course, also high school teachers) who are trying to encourage their students to embrace the Mathematical Practices need to have patience. It isn’t easy to change from a “No Child Left Behind” test-prep routine to a student-centered approach. Using I Notice, I Wonder activities can definitely help. For several years Erin Igo (@igomath) and I have worked in her middle school classroom to have students use Noticing and Wondering and last year we worked on using those two phrases in giving feedback to students. Erin worked on giving written feedback to her students Problems of the Week work using only the two phrases,
  • I notice … (and she valued one thing in their submission).
  • I wonder … (and she asked one question hoping students would reflect and revise/add to their submission).
As she worked on this she quickly emailed me what happened in class each day using these three prompts:
  • some gauge of student reaction to what you did (of course, from your viewpoint)
  • some prediction of what students will do during your next session
  • some reflection on what you predicted and what you now observed

It turned out that Erin’s quick (5 minutes tops!) reflection on what happened in class helped her work through the process. I found it interesting to read (and now I have something to look back on and refer to for this post) … but … Erin and I both agree that the time she took to write her own “teacher exit ticket” was most valuable for her.

Here are some excerpts:

day 4
Even after I wrote my summary of what happened today I sat in my seat for a minute and just took a long deep breath and told myself…it’s a process.  I asked myself,  what opportunity could I create for the student to engage?  I know the opportunity is just time…the students need time to adjust to the newness of this in my class and I need to allow the students to go with it!
day 6
I did notice that students were including more ideas in their explanation based on my “wonderings” from previous problems.
day 9
They seem to be more comfortable with getting on (the computer) and reading my replies…now the question is are they really reading my replies?
I know it’s a process and I have to remind myself everyday but I thought maybe the students would progress a little faster.  I do like what I am seeing.  I want to them to interact with each other more.
day 10
I predicted to see the same behavior but I am wondering if I could change my questioning to get them more engaged in the problems and rubric.  I want the students to talk more with each other about the work.
day 11
I think that student get off task because once they have finish the task that the teacher wants them to do…they truly don’t know what to do…because the teacher hasn’t told them.  I think students are programed to follow directions and the moment they feel like they complete a task…they don’t know what to do with their time.  Its almost like we (teachers) have programmed our students not to persevere….
Patience is definitely a virtue and is not easy to have.  I have noticed that with time my students have started to use my Notices and Wonders in their new explanations…without even thinking about it now.  I have to continue to tell myself that this is a new type of learning for the students that they are not use to and that it will take time to get use to…actually thinking on.
day 15
Students were engaged…but trying to finish..answering the questions instead of completely understanding method.  They just wanted to be finished!
[This is the activity Erin was using:  Ostrich Llama Count–Examining Solution Methods]
I thought they would read the method and try to figure out and understand it before answering questions…big mistake!!!  Next time I would structure it into smaller chucks to make it more manageable for the student and make the task feel like it was easier to accomplish.
Suzanne’s response to Erin on day 15
I love reading this! It proves the idea that you never know whats really going to happen until you try it and invariably it takes time to get it to work! (It’s as much a process as the process you’re trying to get the kids to embrace.)

Some of my previous blog posts on the I Notice, I Wonder™ theme:

  • Wooden Legs Videos
  • Moving From Talking to Writing
  • Repeating vs. Not Repeating Is the Question
  • Work
  • Tips on Managing Mentoring
  • Charlie’s Gumballs Scenario Video
  • PoW Teacher Packet Idea
And in December, 2010, Marie Hogan and I had our article Problem Solving–It Has to Begin with Noticing and Wondering published in an issue of the CMC ComMuniCator, the journal of the California Mathematics Council.
Categories CCSS Mathematical Practices, problem solving
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Owning It

by Suzanne Alejandre
August 4th, 2013

I’ve been thinking back to an EnCoMPASS pre-institute activity and a conversation I had in an online discussion forum. Here’s what happened:

The EnCoMPASS Fellows were asked to view this video clip:


4th graders explaining their Eating Grapes solution

They were also given the text of the problem the girls and their classmates were working on: Eating Grapes [Problem #4507]. The Fellows were asked to notice and wonder about what was happening.

What the Fellows weren’t aware of was that:

  • I was the voice prompting the students in the video clip.
  • The two students were in the 4th grade.
  • I was a guest in the classroom.
  • Asking the girls to come to the front of the room near the end of the class period was completely impromptu. I hadn’t known if presenting to classmates was part of their classroom culture. I had listened to them talking with each other before they came to the front and their two-party conversation seemed worth sharing with the class and getting on tape since videotaping students’ problem solving and communication had been my goal of the day at that school.

As I’ve watched the videoclip several more times and reflected I find it fascinating to think about if the two students were comfortable with what they’d written on the papers they were holding. Did they own it yet?

I had worked with the class for a full class period and during it I :

  • was introduced to the class by their teacher – “Miss Suzanne from the Math Forum at Drexel will be teaching the class today!” (It continues to amaze me that teachers allow me to take over their classrooms for a full period. It is really a treat!)
  • told them I would start by reading a story. I read them the Eating Grapes Scenario (no question).
  • asked the full class “What did you hear?” and I quickly pointed to student after student to listen to their response.

(click on each of the photos embedded here to view a larger version)

  • read the “story” again and again asked them to tell me what they had heard and this time generated an “I Notice…” list on the chalkboard. I introduced the idea of “I Wonder…” and we included that in the chalkboard list as well.

Without going back to look at the tapes, I actually am not sure of what I did next! I remember at some point the class decided to work on the question, How many grapes did Angela eat on Monday? And the students were working in pairs or groups of three to find an answer but to also be able to explain their thinking and how they arrived at that answer.

And at one point we talked about strategies and listed those on the board.

I also remember that as I moved around the room listening to the students talk with each other, I was particularly struck by the drawing the girls had on their paper.

I find myself thinking, what helps students own their own mathematical thinking and helps them be confident in their explanations of that thinking? I imagine that time and practice are critical.

At what point in the problem solving/communication process do students really identify with what they write down? What is going on when they have generated something on a piece of paper but then are asked to ”present”? If they had had a document camera (or a SMARTboard displaying a PDF of their work) would the focus have been more on their thinking as they generated the work on their paper and less on re-creating that work (with accompanying explanation) on the chalkboard?

What do you notice as your students present in class? What are the signs that they feel that they own their work? How are you facilitating their process or, in other words, what is working for you (and them)?
Categories CCSS Mathematical Practices, Videos, problem solving
Comments (2)

Mix and Match

by Suzanne Alejandre
July 27th, 2013

Life isn’t simple. From the time we wake up until the time we fall asleep there are always surprises each day. Just when I think I have a handle on what I’m doing for the day, something comes up and I adjust.

I wonder if we try too hard to present mathematics and, in particular, problem solving too simply to our students. Is that why we have a tendency to:

  • bring closure to a problem during a class period rather than using a Take 5 Minutes approach and let time elapse between engagement with a problem?
  • want to help too soon when students are struggling?
  • want to confirm “yes, your answer is correct” instead of asking “why do you think that?” or some question that encourages explanation rather than right/wrong?

In October of 2011 I tried something during a workshop that I’d actually had slip back to the recesses of my mind … but … as I’ve been thinking more about helping teachers use more problem-solving activities in classrooms, it suddenly came forward again.

Here’s what a group of teachers in the workshop and I tried:

  1. Read-aloud scenario: Eating Grapes [Problem #4507]
  2. Look-at-the-picture scenario: Measuring Melons [Problem #5144]
  3. Look-at-the-picture-and-the-graphs scenario: Filling Glasses [Problem #5104]

We spent about 10 minutes on each first noticing and wondering orally and then taking a few minutes to individually write down some things that were noticed and wondered.

[NOTE: Some teachers encourage students to notice/wonder individually before anything is said aloud. Because my own classroom experiences were with struggling learners and I often work in classrooms now with teachers and students who are struggling, I tend to encourage a quick oral exercise of noticing and wondering before we ever get to the point of writing. So many of the students I've worked with would give up and think they can't participate if at first I asked them to write.]

After we had noticed and wondered on those three problems (not finding answers at all particularly because the scenarios didn’t include any questions!) we paused to reflect on the experience.

  • Was it stressful?
  • Were they on overload?
  • Were they considering trying it in their classrooms?

They responded no, no, yes to these questions.

Thoughts?

If you try this, I’d love to hear stories!

Categories CCSS Mathematical Practices, problem solving
Comments (2)

Finding Time

by Suzanne Alejandre
July 24th, 2013

Yesterday as Max and I were planning a workshop we’ll be facilitating in early August a recurring thought came to me — after spending hours of time on problem solving teachers sometimes comment to us, how will I ever find time to do this with my students?

As I ponder this issue, I wonder if at the heart of it is that
  • the teachers realize that the amount of time we spend on one problem is worth the time?
  • there is no apparent transfer from a condensed one-day workshop to a full-year class?
  • teachers’ learning experiences are different from their students’ learning experiences?
Worth the Time
From formative assessment during the workshop and evaluations at the conclusion of our workshops, teachers indicate that the time spent is worth it for them.
Transfer
While teachers would like to transfer the ideas, this seems hard to achieve. So many school “routines” get in the way.
Learning Experiences
Are teachers more likely to be in control of their own learning? Are classrooms/schools ready at this point to have students be in control of their own learning?
 
How can teachers find time for rich problem-solving experiences for their students?
 
Idea: If students are encouraged to take charge of their own learning, our job is not to “lead” them through problem solving but instead to create environments that encourage them to embrace the process. Try the “At the End of the Period: Take 5 Minutes” approach.
Advantages:
  • Using just 5 minutes at the end of a class period is manageable.
  • Starting and stopping reinforces problem solving as a process.
  • Perseverance is also reinforced.
 
Do you see any disadvantages?
 
Does it make sense that taking this approach could reinforce the idea of problem solving as a process and that it’s not something to rush to finish just to be over and done? How might this idea fit within your classroom routine?
Categories CCSS Mathematical Practices, problem solving
Comments (6)

Learning from Watching

by Suzanne Alejandre
April 5th, 2013

Almost two years passed between Annie, Max, and Steve’s Ignite! debuts in Indianapolis at NCTM in April, 2011, before I made my debut. I watched their preparation, anxiety and performances.

I was learning.

In December, 2011, I watched the CMC-North Ignite! talks in Asilomar. I continued to watch, listen, and learn. In April, 2012 Annie, Max and Steve again performed at Ignite! in Philadelphia at NCSM.

I was still learning.

On October 29, 2012 I received an email from Karen Cowe and she wrote,

“You knew that one of these days I’d come knocking.” … “This will be the last Ignite! for me, so it would be great to finally get you up there!”

I decided this was my opportunity to use what I had been learning from watching. One way to cope with the pressure was not to tell anyone at the Math Forum what I was planning to do!

On Saturday, December 1, mission accomplished!

The next day I emailed:

“My Ignite! talk was successful according to several accounts. I was in good company. I was #5 out of 9 [Avery, Jennifer, Harold, Bill, me, Lew, Ruth, Scott, and Mike]. There were about 400 in Merrill Hall where it’s held in Asilomar. Even the balcony seating was full. The good news is that I didn’t even think about that. I can’t really say it was fun but I told Karen Cowe I was honored that she asked me and satisfied that I managed to do it without getting too stressed. As Ruth Parker said to me, she can’t remember putting that much prep time into something that only lasts 5 minutes! I agreed!”

“Well, we’ll see what the video looks like first since I have absolutely no memory now of what I said! It really is an amazing experience. You’re sitting there watching the four that are presenting in front of you and each of their 5 minutes “feels” like a real 5 minutes (or maybe even longer). Then it’s your turn and the fourth speaker comes over, hands over the mikes, you get them clipped on, you walk over to the spot, and suddenly you go into time warp and it all speeds up so quickly — it’s really, really weird — it all seemed over in about 5 seconds.”

Now that I have proof that I actually did it: Suzanne Alejandre at CMC-North Ignite I know that I really belong to the Math Forum Ignite! Club.

And, as often happens, I am thinking of connections between my experience of watching and learning and how that might play out in a mathematics classroom. There are students who may take time before being ready to perform. Are they watching? Are they learning? When they’re ready, will they perform? I believe there are and they definitely will. And, as I talk about in my own performance, if we create classroom environments to help unsilence their voices, there is even more of a chance that they will perform!

Categories CCSS Mathematical Practices, Videos, problem solving
Comments (2)

Unsilence Students’ Voices

by Suzanne Alejandre
October 3rd, 2012

When I decided to write an article with the title Unsilence Students’ Voices I thought long and hard about using “Unsilence”! Every time I typed that word the text editor underlined it in red reminding me that it was not a “real” word. Was I rebelling against that red underlining? Maybe! I decided that it expressed what I wanted to communicate and so I went with it. I’ve now had the article published in the journal of the California Mathematics Council, the CMC ComMuniCator:

Unsilence Students’ Voices, September 2012, CMC ComMuniCator

I’ve presented these sessions with the title, Unsilence Students’ Voices:

November 2-3, 2012, in Palm Springs, CA
California Mathematics Council – Southern Section (CMC-South)
Suzanne Alejandre and Marie Hogan
Session 120: Friday 8:30 – 10:00
November 8-10, 2012, in Rye Brook, NY
Association of Mathematics Teachers of New York State (AMTNYS)
Suzanne Alejandre and Bushra Makiya
Session 42: Thursday 3:00 – 4:00
November 30 – December 2, 2012, in Asilomar, CA
California Mathematics Council – Northern Section (CMC-North)
Suzanne Alejandre and Marie Hogan
Session 335: Saturday 11:00 -12:00
Ignite!: Saturday 7:30 – 9:00 (link to video coming soon on Key Curriculum’s YouTube page)

As you read the ComMuniCator article and/or view the resources linked from the sessions, please comment here. How are you helping your students make their mathematical voices heard?

Categories CCSS Mathematical Practices
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Connections

by Suzanne Alejandre
June 3rd, 2012

For as long as I can remember I’ve enjoyed having thoughts and tasks and projects overlap and connect. One overlap that happened recently was because of the work Annie and I were doing at Universal Bluford Charter School. The videotapes we made connected with work I was doing to support the Mathlanding project (a grant with Maryland Public Television) and, in turn, connected with having examples of work that we’re doing in classrooms to show to potential publishers of a book we’re drafting about problem solving and communication. Having those connections encourages reflection and deepened purpose. I think one reason I’ve always enjoyed recognizing connections and taking advantage of them is that whatever I’m working on seems to get better each step of the way — it lengthens into a process instead of an isolated event or task.

In 1995 when I first connected to the Math Forum, Steve Weimar introduced me to Connections. It was how we started each morning of the Summer Institute. I had a feeling that there might be residue from one of the institutes and I just found Steve Means description online:

connections webpage explanation

Do you use some idea of Connections in your work? How might a teacher use the idea? How might a school use the idea?

Categories CCSS Mathematical Practices
Comments (2)

An Opportunity

by Suzanne Alejandre
March 25th, 2012

On Friday, March 16, I had the opportunity to hear John Ewing’s keynote “Who Owns the Common Core Standards?” at this year’s Long Island Mathematics Conference, Limaçon 2012.

His message resonated with me for several points that he made:

  • describing the standards as having a focus on the practices as well as understanding mathematics
  • there are dangers if we only focus on data driven education because student achievement cannot only be measured in test score data
  • education is complicated with many goals intertwined (facts and skills, understanding, creativity, attitude, curiosity, lifelong learning) and it is that broad view of education that is important to us as teachers/students

He ended on a positive note:

“This is your opportunity to show…
…that teaching is a profession
…and that teachers are in charge of that profession.”

He encouraged us not to miss this opportunity.

On the blog The Opportunity Equation, you can read a post by John Ewing on this topic: The Common Core Math Standards: Implications for Teacher Preparation.

If you agree with Dr. Ewing and you are looking for opportunities — I offer you this one if you are a Kindergarten, 1st grade, 2nd grade, 3rd grade, 4th grade, or 5th grade teacher or if you work with teachers working with students at that level. Visit the Math Forum’s new blog:

Elementary Mathematics Practices

What do you notice? (leave a comment) What do you wonder? (leave a comment with a question). Don’t miss the opportunity!

Categories CCSS Mathematical Practices, announcement
Comments (1)

Is Math Communication “real” Learning?

by Suzanne Alejandre
June 4th, 2011

This morning I was again looking through my Philosophy of Education paper and I found two paragraphs that I had written in 1986 as I described thoughts I had had as a conversational English teacher for Berlitz School of Languages:

“At Berlitz we learned that to teach a language you must build a relationship with the student. Somehow that student must want to talk to you. We know how to teach people a minimum of vocabulary, but what is more important is the rapport that you build.”

“Many of my students ask me, ‘When will I be able to really speak English?’ When they ask that question, I know that they are on the wrong track and I try to make them see that they should use learning English as a communicative tool and not for quantifying and marking down how much they know.”

As I reflect on the work I was doing the last two days in a middle school, it starts connecting to what I wrote long ago and have continued to believe is important in teaching. I was a visitor in sixth grade classrooms. I had organized the students into groups of three and after giving them a Problem of the Week (PoW) I asked them to talk about it using as much math vocabulary as possible. The sixth grade teachers I was working with had told me they were finishing a unit on probability and the PoW we had chosen was on that topic. I was encouraging students to use math as a communicative tool and they were able to successfully have conversations with each other about math.

I wonder if the teachers the whole time I was doing this with their students, had in the back of their minds “When will my students really speak Probability?” Were they thinking about quantifying and marking down how much their students know or were they listening to how the students were communicating?

In our climate of testing can teachers ever be a little “out of control” or is it only true that important learning is, must be, and can only be the result and product of teaching. Is what we learn for ourselves trivial?

Categories CCSS Mathematical Practices
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Lumps of clay versus sprouting seeds

by Suzanne Alejandre
April 5th, 2011

Last weekend I found myself sorting through some saved papers, books, and magazines and I ran across a paper I had written for a History of Philosophy of Education course that I took as a requirement for my Master’s in Education. Sitting on the floor in our upstairs office I read through the paper and thought, “Wow, I still believe in everything that I wrote even though it was 1989 when I submitted that paper.” Of course, it helps that I wasn’t “young” when I wrote it but was 39 years of age with some classroom experience and my own sons were 10 and 12 years old and so I had had plenty of time to form and also confirm my own personal philosophy. In fact, the title of the paper was “Personal Philosophy Paper.”

Here’s how it started…

“I was a seed. My father thought of me as a lump of clay. The educational system that I work in was formed on the thought that the students are lumps of clay. I work within that system knowing that the students were seeds that have sprouted into a variety of plants. The seed analogy assumes that a unique individual is born into the world to be helped in life in order to grow, learn, and flourish as an individual. The clay analogy assumes that all people are born to be taught and molded into educated adults. I have recognized these two distinct views for a long time but the two analogies are perfect to describe them.”

I thought back to when I had written that paper. I was teaching mathematics at a junior high school in southern California. I remembered thinking that many of my colleagues approached teaching with the thought that a student in their class “didn’t learn” something until they had “taught them.” In contrast, I often wondered if my students had some understanding of a topic before I launched into any section of a unit. What had they already learned about fractions? What conceptual understanding did they have? What misconceptions did they have? What should be the best starting point?

Twenty-two years later … I often find myself working with teachers in their classrooms. Sometimes they don’t start a unit by finding out what their students already know. Is it because they believe that students are “lumps of clay” or is it because they’ve just not developed ideas of how to nurture the seeds of student thinking?

Categories CCSS Mathematical Practices
Comments (12)

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