Some more reflecting

Last week I asked my students to do a final reflection on Grade Six. I gave them a google form that asked four questions:

  1. Rate your year
  2. What is your favourite memory?
  3. What is one thing that you loved about the year?
  4. What is one thing that you would change?

It was amazing to hear their words and voice through the form. I loved the honesty and it really has me thinking.

The questions that I focused on was what did you love and what would you change. Here is the response to what I loved:

Screen Shot 2016-06-26 at 10.18.04 PM.png

What really struck me were two things:

  1. They loved the use of technology
  2. They loved their freedom

Technology struck me because you often assume that these children are growing up in a digital age, shouldn’t they be used to using technology? But that really isn’t the case. Sure they are digital consumers of things but they don’t really know how to use it. In addition, I know that we have the tech in the classrooms but it isn’t always being used. I know that it is more but many teachers are hesitant to use it because we ourselves have no idea what to do with it. But what this really shows me is that our students don’t really know what to do with it. It shows me that we still need to teach them proper digital skills to create and use technology for educational means. They need to learn and be taught how to harness the power of technology and not just use it in the classroom. The kids want to use it they just need to know how to apply it.

The last part really struck home. This year I have been experimenting more with allowing my grade sixes to have the freedom to choose the path that they want. I want them to be in charge of their learning. The more I teach the more I am getting tired of pushing curriculum and telling students how to learn. I want my students to learn because they want to learn. I want them to be in school because they want to be in school. I know that we have a curriculum to teach and that it was made with good solid research but I still want my students to feel empowered by it and not because I put on a song and dance. This year I have tried a variety of things from rearranging my classroom, passion projects, to doing badging and going gradeless. It is great to see my student are loving those changes, that they actually made an impact. It’s amazing to see when you turn things over to your students what and how they learn. They are amazing people.

I was also equally shocked by what my students said they wanted to change:

Screen Shot 2016-06-26 at 10.29.26 PM.png

A lot of it centered around working in groups for math. I think I need to do some more work around how to work in groups and why we work in groups. Though I also wonder if students need some time alone to think. It reminds me of the book “Quiet.” Do we as teachers sometimes forget about those quiet moments where we reflect or think on our own? I know that group collaboration is a skill but so is working on our own. Do we give our students enough balance? I also loved the line about more homework, had a chuckle with that one.

Overall, this year has been about showing my students that they have a voice and that they are in charge of their learning. I want them to be comfortable in who they are, and know what they need to do in order to learn. I did ask one more question and that was what is one piece of advice you would give next year’s Grade Six. I did smile a little when I saw the responses because it was exactly what I was telling them all year, “Be bold, Be Brave, Be confident!”

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What would your students say about their year?

 

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My 2ndish attempt at using provocations

I would like to think that I teach through Inquiry.  I really try to keep all of my work about the kids and their thinking; however, I do find myself still leading discussions more than I would like.  Then I learned about provocations.  WOW! I know that I have previously blog about this subject but since that time I have tried to use them more.  Today in science I did just that (at least I hope I did).

Here is what I did:

1) I got a bunch of experiments working on air and water

Center 1: AIR

Center 2: Water
Embedded image permalink
(note: some of these items were for other provocations)
Center 3: Water Cycle
Center #4: Pollution
I then broke them into groups had books and iPads at the centers and asked them what do they observe?  Wow, I couldn’t believe the talk, the focus, and  the engagement.  Take a look at this shot:
Here the students were so engrossed in what was happening that they didn’t even notice me.  They were saying, “cool look its raining!”  They were also using the vocabulary that we have been building before this through our watercraft project.
What did I learn?

1) Inquiry (true inquiry) is allowing planned exploration.  Students really need time to explore and make observations about the subjects.
2) This takes a lot of planning.  I been planning this for some time now (many thanks to my amazing PLN for their help in this).  As I have been planning I had to think about questions, get all of the materials ready and even think about possible misconceptions.
3) True assessment.  I was amazed at what the students had absorbed through previous books, the Watercraft project and our discussions.
4) Its a lot of fun to watch the joy and engagement of true learning
So if you haven’t done provocations before, give it ago.  Its a lot of fun and you would be surprised at what you will learn about your students.

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



Place Value

These last few months we have been focusing on place value. Place value is such an important beginning for any primary student in mathematics. We have started the unit with basic counting. Now this may seem too basic and you may think, “what kid doesn’t know how to count by grade two?” This may seem an obvious skill to many but it is something that many (not some) still struggle with.

 Counting goes beyond being ale to tag each object and say its corresponding number. By grade two students should be seeing groups of objects, especially twos, fives and tens, and be able to count by them efficiently and effectively. Students are still grasping with recognizing fives and tens as they count often still counting by ones till they get to five and then putting that aside. Students should start to see 5′s as 2+3 or 4+1 or even better 10′s as 9+1. 5+5, 2+8, 4+6, 7+3, without having to count.

 To help with this we have been collecting and organizing objects in our classroom. Students have been counting bins, pencils, books, etc. in order to tell me how many is in each basic. We then moved to figure out how many bundles of tens there was in each basket and if there was any patterns we noticed in the numbers. Students soon realized that the number (or numbers) to the left became the amount of groups of tens. I told them that this was because that is called the tens column in the place value system and really it is saying 1 group of 10 or 1 x 10.

 We are now trying to see how many groups of fives and tens there are in the bins. Now again, I thought to myself this should be an easier concept. Obviously if they see the fives then they will see how many tens. I also thought that since we worked on doubling so much in patterning that they would see that there was two fives in one ten. However, I was wrong again. Like many students, we are struggling to see how one group of objects can be called a 1 group but still be 5 or 10 things. Another mistake that my students are making is assuming that the ones place value tells us how many tens we have. They assume that if the left column told us the tens then the right must tell us the ones. We are currently working on this concept by looking at numbers and asking how many tens and how many fives? The follow up questions are simple: What patterns do you notice? Why does this occur? My hope is that students will see that there are two fives for every ten and if the leftovers (after making a group of ten) is greater then five it is just one more group. Example: 76: The number 76 has 7 groups of tens because there is 7 tens in 70 (10+10+10+10+10+10+10=70). We also have 15 fives because there are two fives in one ten and we have 7 tens so you double it; however, we also have 6 leftover which can make another group of five; making the total 15 fives, with one leftover. 

 To help out at home, keep practising the subutizing plates (dot plates) or counting objects in the house and looking for patterns.

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?

Dot Plates

It has been an amazing experience working with Dot Plates.  Such a simple exercise but what rich discussion we had.  In this simple exercise my students learned about subitizing, counting on and one to one tagging.  They also learned that numbers are made up of other numbers and that there are parts to numbers.  This is the foundation for addition and subtraction.  If you want to create your own dot plates all you need are simple 35 paper plates and bingo dabbers.  The patterns are simple here is a youtube video to follow:  http://www.youtube.com/watch?v=POSgVl07Go0.   Our next move is to play a game called part-whole Bingo. I’ll fill you in on how that goes in my next blog.

Reflection on Classroom Practise and the types of Talk moves/ Questions I ask

I am in the process of analysing my research for my thesis.  My thesis is on the impact my questioning had on student learning of fractions.  I was quite surprised at the amount of questions I asked and the types of questions I asked.

 Have a look at the chart below:


Types of Questions
Amount of Times Asked
Talk Move
Big Idea
Both
Doesn’t initiate any discussion
T- Building on
49 (16.9%)
49
T- Introduce new strategy that has not been developed
14 (4.8%)
14
T- direct teaching
27 (9.3%)
27
T- Go Beyond
75 (25.8%)
75
T-Compare
2 (.68%)
2
T- Initiation- response- evaluation
7 (2.4%)
7
T- Interrogation
73 (25.2%)
23 (31.5%)
50 (68.5%)
T- question unclear
3 (1%)
3
T- Scafolding
32 (11%)
32
T- shares strategy
8 (2.7%)
8
Total of Questions:
290 (49.3%)
31 (10%)
222 (74%)
37 (12.8%)
T- Air Misconceptions
27
27
T- answering with another question
32
32
T- Echo’s students words
15
15
T- Letting students just talk
9
9
T- Monitoring students
22
22
T- no confirmation/ in order to push beyond
14
14
T- relate back to context
7
7
T- relate to other problems
11
11
T- Revoicing
39
39
T- Student revoicing
5
5
T- Think, Pair, Share
19
19
T-Wait Time
27
27
T- Checking for understanding
71
71
Total of Talk Moves
298 (50.7%)
24 (8%)
40 (13%)
234 (78.5%)
Totals altogether
588
55 (9.4%)
262 (44.5%)
234 (39.8%)
37 (6.3%)

The chart is split into two different groups Questions (in black) and Talk moves (in red).  I tallied all of them together and in a three week unit I ask or did a total of 588 talk moves/questions.  This first of all surprised my that I ask or did so much.  Most of the time we often think of teaching as just standing there and lecturing, not getting the student involved.  however, that wasn’t the most surprising stat.  What really got me going was that even though I may have done more talk moves then asked questions the majority of these actions were related to a big idea.  I wasn’t just trying to get the kids to talk about the subject, I wanted them to articulate a big idea of point in mathematics.

So I ask you to think about your practise.  What types of questions are you asking?  What are you doing to make your students talk?  What is the majority of your time in a unit spent on?  Just some things to reflect on.