We're NOTICING and WONDERING to explore Math Tools!!

If you have read my previous blogs you know that I'm pretty obsessed with NOTICING and WONDERING.  If you do not know about this strategy, scroll down to my first post about the strategy.

This past Friday I was privileged to be a part of a first grade classroom that was NOTICING and WONDERING on the 3rd day of school (in fact several of my grade 1 classrooms did this)!   I absolutely LOVE to see the students and the teacher's responses the first time they notice and wonder so I was thrilled to be apart of this.
 
In the class I was in the teacher was having her students explore 5 different manipulatives/tools that they are going to be using in math this year.  She gave each group a box of the manipulative and a piece of large paper that looked like this:

One column asks students what they NOTICE about the manipulatives and the other column asks them what they WONDER.  I typed up this copy so you could see it better but the teacher just hand made the posters on large paper using markers and it worked just fine.  

Students were divided into groups and asked to explore the manipulative and write down what they noticed and wondered about the manipulative.   They were also told that at the end the class would discuss how they might use each manipulative in math this year.   

By the time all students had rotated through each station all of the chart paper were FILLED!!  This was quite amazing to me as many first graders still struggle with writing this early in the year.  The teacher, through observation during the process, noticed that most of the things that students wrote were noticings, even the ones in the wonderings column.  So, in the wrap up, she took time first to help students understand the differences between the two.  The students defined noticing as things that they see, hear, feel, and touch.  Wondering was much harder - many students said it's things you "think".  Which is true but, ideally we were looking for the fact that wonderings are questions that you think.  This is a hard concept for very young students because they just want to give a statement, as opposed to a question.   With practice they will get better at it.    The teacher then took time to discuss some of their noticings as well as their ideas about how they might use them.  

I felt like this was a really fabulous way to explore the manipulatives as it forced students to look at the attributes of the tool and how they might use it.  For example, with the math racks this class noticed that:

• there were 10 beads on each row
• there were 5 white and 5 red beads on each row
• there were 20 beads total
• that by have 5 red and white beads they could "count on" instead of "counting all" the beads

When these teachers go to use this tool students will already have some ideas about how it will help them to count, add, and subtract!  

Bravo to these teachers for using this strategy to help students begin to explore tools that they will use in math this year!  

Back to school....consider asking these questions

How many of you ask your students, "What did you do this summer?"    If you do, read on and consider these questions instead of the age old question of what they did this summer.

Jenny Froehle, in her blog suggests that in this tech age when we are tasked with growing students as problem solvers and critical thinkers we should rethink the questions we ask students.  She suggests the following questions and a few different ways to ask them.

Keep in mind that these questions are not geared to one specific grade band so, the language or the way they are asked may need to be modified for your age group.

I agree with Jenny when she talks about the need to help students:

• identify and quickly understand a need or problem,
• creatively design solutions,
• analyze what it takes to build answers,
• collaborate with others,
• communicate findings and results,
• critique and revise without fear, 
• know where to go to learn what they need to solve a problem or complete a project,
• etc....

These questions push us to help kids start "digging deeper" and actually apply and transfer their knowledge in real world kinds of ways.  

When I read Jenny's blog post I was really struck by how we can take simple "back to school" questions and make them so much more in-depth teaching questions.  I can't take credit for most of this, I just summarized and reformatted much of what she shared.

As our teacher's getting ready to go back to school TOMORROW...I couldn't help but share these thing.  I want to wish all of our WCPS teachers (you know who you are) a wonderful start to the 2015-16 school year!  

Thinking about your math instruction? Consider this...

First let me say, that because I have spent the last 10 years in elementary school (and before that 10 in middle school), much of what I'm going to write is from that perspective but know that this is not exclusive to elementary classrooms and it is something that middle and high school classrooms need to think about as well.

Most of us realize that the way we were taught math (sit and get or chalk and talk) is not effective for most students today (or then for that matter).  In a push for differentiated and/or individualized instruction many teachers have ditched the notion of whole group instruction and opted for 5 day a week small group instruction and/or centers (or workstations).    I applaud teacher's creativity in trying to help students learn more math content in a student centered conceptual way but....have we increased the application or transfer of that content through the sole use of small group instruction?  While we are presenting the material in a more engaging way (games, less worksheets, etc...), are we really teaching kids to understand math and apply or transfer those concepts more than the old traditional ways of math instruction?

The beauty of the Common Core and the thing that I believe ties all of the new standards together, be it Next Gen, C3, Math or ELA CCSS, is teaching in an inquiry based way so that students become problem solvers and critical thinkers.  Honestly, if you have attended on of my workshops, you have heard me say at least once (if not a dozen times), "If my kids only take away a few things from math instruction, I hope it is the Math Practices because if they are proficient with those habits of mind they can do anything"!

Consider this, how are we building those Math Practices in small group and centers?  I think some of that can happen there but I think that critical thinking and problem solving is best learned from each other in whole group settings as well as the teacher.  Often when teachers group students for centers they are placed in homogeneous groups.  But, I contend that students learn these critical thinking and problem solving skills for students of all levels.  Some of our "lowest" math students tend to "think outside the box" where some of our "high" math students are very linear in their thinking - both groups of students can benefit from each other.

So I'm not saying do away with small groups....I'm advocating for a BALANCE of whole and small group instruction.  There are benefits of both.  

What should that whole group instruction look like?  It should be filled with things like Number Talks, 3 Act Lessons and other intriguing problems to solve, open-ended problems, Noticing and Wondering, etc...  This should be a time where students are collaborating, working together, and sharing.    Most importantly this time should end with at least 10-15 minutes of whole group sharing of learning, questioning, and thinking aloud together.     Teacher's don't need a page of math problems for this -- they need 1 or just a couple of good ones!

This whole group time should not just focus on the content but the thinking as well.  I worked with a fabulous group of grade 5 magnet students (with a wonderful young teacher) for a 3 Act Lesson this year.  These kids had lots of math SKILLS!!!  They knew how to do math but, not surprising to me struggled to solve a problem that they generated in a 3 Act Lesson.  They were quick to "erase" their thinking if it didn't seem to work out.  When I noticed this, we stopped and had a quick whole group discussion about the value of analyzing what went wrong and just setting it aside in case they might need some of those calculations again (this is something we also talked about it in the conclusion of the lesson).    These students also did lots of calculations but didn't label much and therefore struggled when they had to explain what they did to remember why they did those calculations.  We talked, in the end about how solving this problem was a lot like doing a science experiment - if the math didn't work out we had to analyze what went wrong and then determine another path to take to solve the problem instead of just scrapping everything and doing something different or giving up.    Their teacher told me, after the lesson, that his kids didn't so much learn new math that day but they really learned the value of analyzing one's thinking and communicating in a more concise way, their thinking through what they wrote on paper.    He told me that the kids really enjoyed the lesson and learned so much that they could apply to future problems.

So, what should the teacher's role in these whole group sessions be?  The teacher should be the facilitator and questioner.  The teacher doesn't even have to have the "answer" to the problem - the teacher just needs to know how to question kids when they get stuck and when to stop and talk about the problem solving methods (as needed).  The teacher also needs to skillfully set up the class to help kids develop those habits of mind - whether to use pairs, small groups, and when to use protocols to cross pollenate those ideas.  

One of those ideas that I use to cross pollenate ideas is called "Send a Spy".  Often if kids are working in small groups I will stop them and tell the groups that it is time to "send a spy".  Sometimes I appoint the spy in each group and sometimes I let the group choose.  Each group send their spy to look at the work of other groups as they continue to work.  We have rules for this...no one can cover their work, the spies aren't allowed to write or talk until they get back to their group.   They only have about 2-3 minutes to do this - I usually play some "spy music", like the Mission Impossible Theme while this is going on.  When the music stops they have to return to their group and share what they learned.

These are just some of my thoughts on the structure of math time.  Honestly for me, in an elementary classroom I would have 3 days of small group instruction and 2 of whole group each week.

If you want to learn more about teaching problem solving be sure to read Max Ray-Riek's book, Powerful Problem Solving.

Agree...Disagree with any of this?   Want me to elaborate on any of this?   I'd love to hear from you!  Leave me a comment!

Noticing and Wondering with Pictures

Noticing and Wondering is a strategy that can be used with "word problems" (oh how I hate that we call them that, but that's something I'll address in a future post) as well as with pictures, graphs and infographics.    Today I will focus on using a picture.  Here is an example from Dan Meyer's site:  101qs.com:

This particular picture would be good for grade 6 (common core) as it is intended as a unit rate problem (how much per push pop).  

To use this, simply project this picture or share it with students on their electronic devices.  Then have students take a few minutes (2-3) on their own to start writing down things they NOTICE and WONDER.  

Next have students take turns sharing with a partner or small group.  Sometimes if I have them share with a partner when I go and share out with the whole group,  students who are called on have to share something their partner noticed or wondered instead their own thinking.  By having students share their partner's thoughts this puts more accountability on their partner sharing.  

As a whole group we share the wonderings and then come up with a central question to investigate as a class.  Questions students may generate with this picture are things like:

• How much does one Push Pop cost?  (unit rate)
• How much should sell each Push Pop for in order to make a profit (if you were buying these to resell)?
• How much would it cost to buy all of these packs of Push Pops?
• etc....  

For this picture I would have the class choose one question to have everyone investigate and then if they get done and want to continue investigating other questions, they may.  Sometimes we run out of time and kids are just don't want to stop.  If this happens I would have students write the question(s) they want to continue to investigate down in a individual or classroom "Unsolved Questions/Mysteries" binder.  These questions can then be revisited when students have time in the future.  

I almost always allow students to work as partner's and/or small groups.  Even if students are working together, want each person to capture their response to the question independently. By having all students record they are accountable and it helps them learn to communicate their thinking (Math Practice 6). 

If I decide to have kids use a rubric to rate each other, or I decide to use a rubric to score them, I am sure to provide the rubric expectations and criteria before they start working.  Some of the rubrics I have used for math are found here.   For this particular problem I may score them on how they precisely communicate their thinking. 

Once you start NOTICING and WONDERING you will start to look at the world a little differently.  I'm always taking pictures of things that I think could lead to doing some math.    Now that I almost always have my iphone - I always have a camera handy.  Kids can also take pictures that would lead to "doing some math".  

If you students are getting really good at NOTICING and WONDERING I suggest progressing onto Three Act Lessons (see my post below).  I always have my kids NOTICE and WONDER as part of Act 1 of the Three Act Lesson.  

I hope this has given you some more ideas about NOTICING and WONDERING!  Feel free to let me know if you have questions or need clarifications! 

Happy Last Days of Summer!