Can we truly have a student led lesson?

My students hard at work on a class project. Focus: Why do people Come to Canada?

I have heard these terms (student led and Student choice) being used and it has started to make me do some thinking. My biggest problem that I am having is if we as teachers are making detailed and thoughtful lessons, can we truly have student led lessons?

Now I know I may be questioning or going with the flow but, hear me out. I understand that as teachers we need to have the voice and ideas of the students at heart of our lessons. Teaching is no longer about the wise old sage on the stage giving all of their knowledge to their students. but should be more about facilitating the learning that is happening. If that is what you mean by student led then I am all for that. However, let me push some thinking more here.

In the last three years I have been highly influenced by Stein et al. article titled: Orchestrating Productive Mathematical Discussions: Five practices for helping teachers move beyond show and tell.  In this article they showcase five practises that all teachers should be doing.

11: Anticipation (P.322)

The first thing is for the teacher to look and see how students might mathematically solve these types of problems.  In addition, teachers should also solve them for themselves.  Anticipating students’ work involves not only what students may do, but what they may not do.  Teachers must be prepared for incorrect responses as well.

2: Monitoring students’ work (P. 326)
While the students are working, it is the responsibility of the teacher to pay close attention to the mathematical thinking that is happening in the classroom.  The goal of monitoring is to identify the mathematical potential of particular strategies and figure out what big ideas are happening in the classroom.  As the teacher is monitoring the students work, they are also selecting who is to present based on the observations that are unfolding in the classroom.

3: Selecting student work (P.327-328)
            Having monitored the students, it is now the role of the teacher to pick strategies that will benefit the class as a whole.  This process is not any different than what most teachers do; however, the emphasis is not on the sharing, but on what the mathematics is that is happening in the strategies that were chosen. 
4: Purposefully sequencing them in discussion (P. 329)
With  the students chosen, it is now up to the teacher to pick the sequence in which the students will present.  What big ideas are unfolding, and how can you sequence them for all to understand?  This sequencing can happen in a couple of ways: 1) most common strategy, 2) stage 1 of a big idea towards a more complex version or 3) contrasting ideas and strategies.

5: Helping students make mathematical sense (P.330-331)
As the students share their strategies, it is the role of the teacher to question and help  them draw connections between the mathematical processes and ideas that are reflected in those strategies.  Stein et. al. suggest that teachers can help students make judgments about the consequences of different approaches. They can also help students see how the strategies are the same even if they are represented differently.  Overall, it is the role of the teacher to bridge the gap between presentations so that students do not see them as separate strategies, but rather as working towards a common understanding or goal of the teacher.

If we follow these practise as teachers we are thinking about good contexts that will create huge discussion in our classrooms. We are anticipating results and answers so that we as teachers can ask the right questions at the right time. We are planning and sequencing work so that the end results end up close to the Big Ideas that we were hoping to accomplish and we as teachers are prodding, questioning and revoicing so that the Big ideas are brought to the students attention. Finally, we then create similar problems so that students have the opportunities to try these ideas out again.

Now I know that this article is a math article but these practises can be and should be for all subjects. So if we follow this line of thinking, who is really leading the lessons? Is it the students? or is it the teacher? If we as teachers are putting in this much thinking and planning do we truly have student led or based lessons? or is it because we have put all of this planning into our lessons that students feel that the lesson is student based and that is really all that matters?

Love to hear your thoughts.

Making kids doers of math instead of Doing math!

I have been thinking about this topic for quite some time now and then when asked to do the OAME 2015 ignite I thought this would be an amazing topic to push thinking.

My biggest fear in education right now is that we are having our kids go through the paces of doing school. We our turning our students through the drudgery of school.  Before I started to really question this thinking I saw it in my own class. My students were coming to school going through the paces and then leaving. Sure they enjoyed it but was I really making them think? What type of work was I making them do? Why was I teaching them these skills?

I then came across this statement by Fosnot:

The purpose of teaching is to learn, but without learning there is no teaching!

I was shocked. Was she saying that if my students didn’t learn then I wasn’t being a good teacher. The answer was yes! And the more that I reflected on this the more I agreed with this statement. Over time, i realized that even though I was teaching different kids the common denominator was still me. So when I asked questions like, why don’t they get this? The answer was because I am not doing a good enough job. I wasn’t making them understand because I was just making them be there instead of embodying the learning.

I see this a lot in math and this is partially because of my lens. In a math class we traditionally stand I front of students, give a lecture, let them work and then test them to see if they understand. B how many of our students are really learning? How many of them become mathmaticians? 

VanDeWalle suggests that The goal is to let all students believe that they are the authors of mathematical ideas and logical arguments.

So then how do we go about doing this?
I would like to propose three key points to this:  Link back to my thesis always link back

1) Role of the teacher
2) Environment of Learning
3) Accountable Kids

Role of the teacher

I want to first preface that teaching to me is about turning my kids into mathematicians through inquiry and exploration but I start with this point because as a teacher we have the most critical role to play.We are not to sit back and allow our students free reign but to ignite (lol) and actually talk about math. I know really insightful!

Researchers have suggested that children should being engaged in problem versus talk procedures. But our role is to bring out the math not by telling students information and expecting them to regurgitate it but by creating contexts for learning asking critical questions and debriefing the math. In my research I found three types of questions that worked the best for creating these conditions:

1) Interrogation: Just like the title suggests → a lot of why’s and how comes2) Going beyond: Pushing the thinking beyond the schema the student has created. These questions include, have you thought? What about this? Can someone else explain3) Comparing: Often I compare strategies together to see if students can move from one to the next. This includes, what are the differences? Similarities

In order for this process to really work “Teachers must have the [student learning] in mind when they plan activities, when they interact, question and facilitate discussions” ~ Fosnot pg. 24

The key to everyone one of these questions is that it was linked to a big mathematical idea. One that was key to the learning of the student. The same goes to the various talk moves that a teacher can make. These should include: Wait time and revoicing. I cannot stress how important these two items are to the success of building mathematicians. To often we don’t give students enough time.

Creating an environment of learning

In a mathematical environment , students feel comfortable trying out ideas, sharing insights, challenging others, seeking advice from other students and the teacher, explaining their thinking and taking risks. ~ VanDeWalle pg 36. When students do mathematics in an environment that encourages risk and expects participation, it becomes an exciting endeavour. Students talk more, share more ideas, offer suggestions, and challenge or defend the solutions of others. When a context is real and meaningful for children, their conversation relates to the context. They mathematize the situation. ~Fosnot

Making kids accountable:

No one is allowed to be a passive observer ~ VanDeWalle pg 36

I love this quote. I think it is exactly the whole idea around accountable talk. Many teachers may think that just because the student is not talking they are not participating but the key is not to be a passive observer, which doesn’t always involve talking but listening. However, that has not been the case in school. We have been so use to hearing teachers talk that many of our students are use to being told the answer that they are not use to talking. 

In my thesis research I saw that when I asked an Initiate respond Evaluate types of questions (basically questions I already knew the answers) I got no further discussion happening. My kids just sat there. But when I asked going beyond types or comparing questions, basically critical thinking questions, that was linked to big ideas kids talked about math.  They became active users of the information and doers of math not just following the paces.

So I guess I want to ask: How do you make your students into Doers versus just doing? This question doesn’t need to be math as it is a broader problem in education. Love to hear your thoughts and ideas.

Why teach through inquiry? A real testimonial

Now I know that I have posted on this subject before but with the day I had I just had to write about it again.  Inquiry: WOW!  Man I love it.

I know that recently there has been a lot of discussion about inquiry in the classroom and if it is really making students learn.  There has also been a huge push to go “back to basics” all I have to say is wish you were in my class (even school) today.  Today’s math problem was quite simple: 
“Mrs. Standring, our proud principal, needs help.  Our school has been open for two years now and we got more kids this year, because of that the fire Marshal has asked her to make a new fire plan.  I was telling her that we were studying measurement and she thought you could help.  How far is our door to the nearest fire door?”
The kids went nuts. It took them a while to get over the fact that they were helping Mrs.Standring.  Well they just started with the questions: what tools can we use? How are we starting? Which door is closer?
Most of them saw that a meter stick would be the best measurement tool, we had been talking about measurements for some time and been measuring in non-standard too and knew that it was inconsistent. So they all grabbed meter sticks and off they went.
We got a bunch of numbers and came to the carpet to discuss. They were all in confusion, why do we have different numbers. We used a standard measurement? We then asked the students to demonstrate how they measured.  Some saw that when you lift the ruler up, you sometimes, overlap the space or leave a gap.  I then asked them how can we prevent that?  This brought up the discussion of leaving marks, or placing fingers.  They went back at it.
Students then came up with an answer but when I asked them to tell our principal they didn’t know what to say.  This of course then led us into a discussion about explanation texts, which we then made some success criteria and off they went to write.  When the bell rang half way through the students were very upset that they didn’t have enough time to finish there work.
Not only did this problem happen in my classroom but my teaching partner did it too.  Her kids thought string was the best and then bring it back to measure against a meter stick.
Now you may read this and say so what? So what! The best part of this is that all this discussion was student driven. All collaboration, student driven, all learning student driven.  Yes as a teacher I am incharge.  I have planned this problem, I have thought of the big ideas and questions but it is the passion, and learning of my students that drive this problem.  Also, when looking back (though I will say to make it worth while this should be done first) my students met over 37 expectations from the curriculum and all of the learning skills that are in the report card.  In addition, the talk was amazing and the learning even more. Not only this but when it comes to assessment I have it all, with no tests.  I know my students skills, next steps and a mark of work.
Inquiry for me is the only way to teach.  Yes, students do need facts and knowledge but that fact and knowledge is gained through the inquiry process.  Also, if a student doesn’t have that to start with as a teacher it is my job to scaffold the question so that they do learn; however, it should still be done in a way that the student is discovering the learning.
Now in the end, there is no wrong way to teach, all learning is valid and good. But through inquiry students do grasb and understand concepts faster and with a deeper understanding. It’s been amazing to see our students development as our school adopts this approach. There is less review needed from year to year and the students are talking more and communicating their thoughts.  For me there are a couple of key reasons to teach through inquiry:
1) Students learn and enjoy the lessons more then traditional teaching styles
2) It covers more curriculum and deeper knowledge
3) Students retain information
4) Learning is integrated in real life, why separate at school
5) It validates the students and makes them buy into their learning. If they are invested you have less behaviours
6) students easily tune a teachers voice out but not their peers
7) It’s fun for me too! Shh don’t tell my students
What are some potential problems: (though to me they are not problems)
1) Problems take time: learning is not easily divided into 30, 40 minute time blocks
2) Can be and should be noisy but productive
3) Takes more planning: yes it takes more planning. You cannot wing inquiry. Even though it may appear as if it is winged or that the teacher is doing nothing it is an art form and requires a lot more planning (will tough on that in a minute)
4) Parents: you will get parents complaining and questioning your practice.  This is new for many and with new comes questions and fears. Stand up and proudly defend your practice because when they hear and see their kids they will love you.
5) you may not have all of the answers
What do I need to do to teach through inquiry?
1) know your content and curriculum: when you know your students learning it is easier to formulate questions and scaffold students learning.
2) plan: I wrote a previous blog post about planning but essentially you need to plan.  Inquiry does not happen by the seat of your pants.  You need to anticipate students questions, problems, and ideas.  You need to know what the big ideas are and where you want the lesson to go.  You need to understand learning trajectories and see where your class is and should go next and you need to do the problem first.
3) inquiry should be contextual and related to the kids life.  The best inquiries are ones in which the students really wonder or can invest in.
4) have fun and don’t be afraid to make a mistake.
Overall, I feel inquiry has been one of the best things I could have done. It really benefits the students and it makes my assessment easier.  I would love to hear your thoughts on inquiry? Have you tried it? Struggles? Pointers? Thanks for reading.

Genius hour reflection #2

So we have been doing genius hour for the past tho months now and though I had reservations about it, it truly has been an amazing experience for me and my students.  For this that do not know what genius hour is, it is basically a moment in our week where students can explore their passions. We do it every day 4, right after technology. My students have been in love with it. In fact many of them have been finishing projects at home.

Now when we first started it, it was a little tough for some of my lover students, they just didn’t know where to go or even how to start. Many of them haven’t even been encouraged to think or explore their own passions (which is unfortunate). It was also a struggle because many of my students didn’t have the research skills to get started.  This being said, with open learning goals, constructive feedback and ongoing discussion I would say all of my students have been working hard, learning and having fun.
Some things that I have learned implementing genius hour in the primary grades:
1) it is a slow process and may not look perfect 1 try, or two or three. Patients it eventually comes together
2) make your students reflect on what they learned and how it went. This was a big aha moment for me. Since making them reflect the students have begun to understand that it is about the learning and the journey not so much the final outcome.
3) genius hour helps with so many other strands and skills.  Part of our curriculum is do learn about celebrations around the world. This can be hard when the majority of the school is from one culture and not very wise about other cultures.  It is hard to be interested in other cultures or have inquiry when you don’t know where to start.  Because of genius hour, I have been able to introduce how to question, how to wonder and the RAN model for reading non fiction. It has help with this project and I think many more
4) Introduce a Wonder wall. This has been a. New learning for me but when kids can post wonders even if they aren’t answered by them they can see what else to explore and help others in the classroom. Many of my students have started other peoples wonders.
5) have technology ready for students to use.  In my classroom we have a set of net books and iPads. Students collaborate, talk and work together to get it done.
Anyways these are just some thoughts on implementing genius hour. If you want more help or just someone to talk to about it just email me or tweet.

Accountable Talk in the Classroom: Practical Advice for the Classroom

I have recently finished one great book and one great article on Accountable Talk and Classroom Discussions. 

Stein, M. K., Engle, R., Smith, M. & Hughes, E,  Orchestrating productive mathematical discussion: Five practices for  helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10313-340. 

Chapin, Suzanne, O’Connor, Catherine, & Anderson, Nancy. Classroom Discussions: Using         math talk to help students learn. California: Scholastics. 2009.


Accountable talk is one of my passions as I have spent the last four year studying the impact it has on my classroom.  I highly reccomend these two readings for anyone interested in learning more about accountable talk.  However, I also know that in teaching we really don’t have time to sit down and read.  For this reason I thought I would summarize them for you and include them in my blog (I appologize in advance as this will create a rather long post).  These ideas come from the two resources above and my own thesis work.  I hope they are practical advice for anyone in their teaching practice.

Implementing Classroom Discussions
Establishing and Maintaining a Respectful, Supportive Environment:
·         LAY DOWN THE LAW (in a collaborative manner):
o   that every student is listening to what others say
o   that every student can hear what others say
o   that every student may participate by speaking out at some point
o   all have an obligation to listen
·         neither student or teacher will participate in bad environment.  Everyone needs to feel comfortable.
·         Emphasize the positive and forestall the negative
·         Establish classroom norms around talk, partner work, and discussions (what does it look like, sound like and what should we be doing)
·         everyone has the right to participate and an obligation to listen
Focusing Talk on the Mathematics:
·         During the discussion time you need to focus the talk on math:
o   plan your questions carefully
o   Have good formative assessment happening at all times
o   Make a plan as to what big ideas you want to cover
o   Anticipate problems and possible solutions
Providing for Equitable Participation in the Classroom Talk:
·         Here are some strategies that will assist you in making it all equitable:
o   Think-pair-share
o   Wait time
o   Group Talk
o   Partner Talk
o   Debates
o   Random  Choice on who Talks

 

Types of Talk Moves:
Talk Moves That Help Students Clarify and Share Their Own Thoughts
·         Say More:
o   Here you literally ask the student to explain more.  “Can you tell me more?”, “Tell us more about your thinking.  Can you expand on that?”; or “Can you give us an example?”
o   This sends the message that the teacher wants to understand the students’ thinking.
·         Revoicing:
o   It is sometimes hard for students to clearly articulate what they are trying to say by revoicing or having a student do this it allows the original student to check and make sure what they said is true or to hear it in a new way
o   It is not just repeating but more of paraphrasing the students ideas
·         Model students thinking:
o   This is not so much a talk move as it is a way to help talk
o   As students talk record what they are saying without comment.  When they are done ask them , is this what you meant?
o   This allows students to reflect and think about what they said in comparison to what was written
·         Wait Time:
o   Wait time is so important.  I cannot stress this enough.  The longer you wait the better responses you will get.  It allows students to process what you or another student asked and be able to formulate their thinking
Talk Moves That Help Students Orient to Others’ Thinking
·         Who can Repeat?
o   I would classify this under the first category but it also helps students with understanding what their peers are saying
Talk Moves that Help Students Deepen Their Reasoning
·         Press for reasoning
o   Here you are basically asking students to think about why they did this.  This can be done by asking:
§  Why do you think that?
§  What convinced you that was the answer?
§  Why did you think that strategy would work?
§  Where in the text is their support for that claim?
§  What is your evidence?
§  What makes you think that?
§  How did you get that answer?
§  Can you prove that to us?
o   Not only are these excellent talk moves but excellent questions that push students beyond their thinking and make excellent mathematical connections.
Talk Moves That Help Students Engage with Others’ Thinking
·         These are excellent questions that help students build upon their own thinking and the thinking of the community
·         Do you agree or disagree…and why?
o   This really brings students into direct contact with the reasoning of their peers
o   You can do this by:
§  Thumbs up or thumbs down
§  Why do you agree or disagree?
·         Who can add on?
o   When you ask this question make sure that you wait for answers as this may need time to develop connections.
1: Anticipation (P.322)
The first thing is for the teacher to look and see how students might mathematically solve these types of problems.  In addition, teachers should also solve them for themselves.  Anticipating students’ work involves not only what students may do, but what they may not do.  Teachers must be prepared for incorrect responses as well.
2: Monitoring students’ work (P. 326)
While the students are working, it is the responsibility of the teacher to pay close attention to the mathematical thinking that is happening in the classroom.  The goal of monitoring is to identify the mathematical potential of particular strategies and figure out what big ideas are happening in the classroom.  As the teacher is monitoring the students work, they are also selecting who is to present based on the observations that are unfolding in the classroom.
3: Selecting student work (P.327-328)
            Having monitored the students, it is now the role of the teacher to pick strategies that will benefit the class as a whole.  This process is not any different than what most teachers do; however, the emphasis is not on the sharing, but on what the mathematics is that is happening in the strategies that were chosen. 
4: Purposefully sequencing them in discussion (P. 329)
With  the students chosen, it is now up to the teacher to pick the sequence in which the students will present.  What big ideas are unfolding, and how can you sequence them for all to understand?  This sequencing can happen in a couple of ways: 1) most common strategy, 2) stage 1 of a big idea towards a more complex version or 3) contrasting ideas and strategies.
5: Helping students make mathematical sense (P.330-331)
As the students share their strategies, it is the role of the teacher to question and help  them draw connections between the mathematical processes and ideas that are reflected in those strategies.  Stein et. al. suggest that teachers can help students make judgments about the consequences of different approaches. They can also help students see how the strategies are the same even if they are represented differently.  Overall, it is the role of the teacher to bridge the gap between presentations so that students do not see them as separate strategies, but rather as working towards a common understanding or goal of the teacher.

 

Trouble Shooting Talk in the Classroom

My Students won’t Talk:

v  First ask yourself: our my students silent because they have not understood a particular question? –> sometimes they need to hear the question a few times and have time to think
§  if this is the case then give students time to think  (wait time is very important)
§  also revoice it or have another student revoice the question
v  Second they may be shy or unsure of their abilities:
§  If this is the case you may need to revisit strategies for talking
§  Think-pair-share is an excellent way to get kids comfortable to talk
§  it will also take time to get kids comfortable.  Wait time again is important as it holds students accountable.  Also making them feel comfortable and that mistakes are okay will assist with this difficulties
The same few students do all the talking:
v  Wait-Time:
§  I know that I say this a lot but it allows the other students to think and then participate while making the ones who always participate  (it will feel awkward at first but wait as long as you can)
v  Have students Revoice:
§  This is good strategy to bring validity to students answers and encourage others to talk
v  Conferencing with the ones who talk a lot:
§  You also don’t want to ignore the ones who talk  all the time.  You can talk to them and let them know that you are not ignoring them but are just trying to allow others to participate.
v  Turn-Taking/ Random presenters/ group discussions:
§  These are all roughly the same strategy.  It allows you to have certain presenters share their thinking without offending or allowing others to take over the conversation
Should I call on students who do not raise their hands?
v  there is research to suggest that students will learn by listening but you will also hinder the class progress in discussion.  To help try creating a positive space that allows all students to feel comfortable and willing to participate.
v  “right to pass”: 
§  allow students at the beginning of the year the right to pass.  You’ll notice that they may do this at first but as you build the community they do this less and less
v  Call on reluctant to students after partner talk:
§  Often when you give them a chance to share first they are more willing to share or at least have a response from their partner
My students will talk, but they won’t listen
v  Set the classroom Norms:
§  remind each students that they have the right to be heard but that this also means an obligation to listen
v  Students Revoice:
§  When students need to revoice then they have to listen
Huh?” How do I respond to incomprehensible contributions?
v  The temptation is to simply say, “Oh, I see.  How interesting….” and quickly move on to another student.
v  Try Revoicing or repeating what they have said.  After you have done this ask them is this what you meant?
v  Record their strategy on the board and ask them is this what you meant?
Brilliant, but did anyone understand?
v  Repeat what they said, then have another student repeat what they have said (if really important have many students repeat)
v  Break the explanation up into small chunks and revoice or have the students
I have students at very different levels
v  Pair students in ability groups:
§   Similar abilities with similar abilities.  This allows students to contribute at their level and to also struggle at their level.  In addition, it allows you as the teacher to differentiate as needed.  When you scaffold you can do so by group not by individuals
v  Parallel Tasks:
§  Give students similar tasks but with varying degrees of difficulty (still around the same big idea)
What should I do when students are wrong?
v  First ask yourself is there anything wrong with having the wrong answer?  Sometimes wrong answers provide rich and meaningful discussions
v  Need to establish Norms around respectful discourse and discussion with wrong answers
v  Mistakes are always an opportunity for learning to happen

This discussion is not going anywhere or Students’ answers are so superficial!
v  This may be happening because you are asking to many students to share or revoice the ideas that are happening in the classroom or in the case of superficial classroom  norms have not been established or the types of questions have been simple and direct
v  Use the working on phase as an opportunity to direct your bigger discussion:
§  As you are walking around and looking at work, look for the progression your students are taking.  This will lead you to a group discussions.  What questions are the students asking themselves?  What problems are occurring?  What big ideas are they trying to work out, have worked out or are struggling with?
v  Look at the type of questions that you are asking:
§  As teachers we are comfortable asking questions but do our questions already have responses?  Are we leading the kids to OUR thinking or our we allowing the students talk to LEADthe thinking.  Yes you are very much in control of the discuss and have to lead but it is not YOUR thinking but THEIRS that should be articulated.
§  Higher order questions build-upon or go beyond the thinking that is being presented.  As a teacher we need to help with the connections in mathematics.  Compare student work?  Compare strategies, Pros and Cons, naming and identifying.  We need to go beyond just show and tell



Patterning in grade two

Today was our first formal lesson in patterning.  What I mean by that is we have been discussing patterns but more in the context of number sense, where we have been learning to count by twos, fives and tens, as well as, doubling numbers. This type of talk has been focused on the magnitude of numbers and associated with place value not so much on growing and shrinking of patterns.

So today we started with a problem that was asking the students to sort eight sets of (patterns and none-patterns) into two categories, a yes it is a pattern and a no it is not a pattern. I have attached the patterns down below.
It was very interesting conversation around this. At first the students put only the repeating patterns in the yes category stating that for it tone a pattern then it had to repeat. I had to remind them about the book we read called patterns big and small. In this book they had a set of nesting dolls, I’m asked the kids did that pattern repeat? After that discussion the kids where better off explaining their reasons for their groupings.
I really liked this question because it made the students really think about what a pattern is and what attributes are needed to make a pattern. They obviously had worked with patterns in grade one but mainly with repeating patterns, which is why they at first they only made piles with repeating numbers.  The non-patterns are also helpful because they can assist us with thinking about what attributes a pattern doesn’t have and therefore in the end has.
Today we are going to be working on the justifying of their answers and then coming up with a definition of what a pattern is and is not.  If your grade two or any grade for that matter I highly recommend this type of problem for your class.

For the patterns we used click on this link: https://www.dropbox.com/s/okxkmomlckfu758/Is%20this%20a%20pattern.docx

 

Making conjectures and proving them

In grade two we have been exploring the concept of doubles and what is a double. It’s an interesting concept because we probably assume that by grade two students should know what a double is and why it is called a double, but that was not so. Oh of course, all of the kids could count by twos, but when asked what makes a double all I got was blank stares.  With this in mind we went through some problems exploring whAt a double is.  We started with the story of Madeline, see previous post, and then moved to a discussion about where we have seen a double before.

Today, the class looked at pairs of shoes.  The problem was if each person in your house had one pair of shoes in the front hallway, how many pairs would you have and how many individual shoes would you have?

Most of the students drew out the people and then the shoes, they then counted by ones or twos to get the individual shoes. This alone is a good math problem but I decided to take it a step forward. I asked them to look at their results and make theory, so that I could figure out how many shoes I would have for any number of people?  Once they made a theory they had to test t out to make sure it was true.

I was amazed at how many of the students looked puzzled. It was almost like I asked them to fly to the moon. I am amazed every year at how students struggle with thinking. We often say that’s we are teaching 21st century skills but are we really?

As I look at what my students eventually did I think how they are starting to become real mathematicians. Sure I could have told them the rule was the amount of people doubled would give you the individual shoes because each person has two shoes or mode the rule with pictures, t-charts and then follow up with a question like, “what pattern do you see?” or i could count the shoes with the kids, but then would my students have learned?

By doing this, this way, I have allowed my students to make their own theories and thentestthem out and prove them to the mathematical community. They have thought about the process, they have looked at the numbers in relation to the context and the math became real.

So I ask you, what are you doing to make your students think?