Thursday, 12 December 2013

Tired of the excuse "I'm not good at math"

I think I have ranted about this before, if not in a blog, definitely in person.  Why is it okay to say "I am not good at math". The most recent occurance happened today.  I was at a local grocery store when I brought up three items for price match.  The three items were on sale 3 for 5 dollars.  The cashier (who was not a young person, not that age matters in this) said "that is $1.20 each right? Sorry I am not good at math."  My reply was no it's 1.66, actually 1.66666666666, so one of them will be 1.67. She look at me confused and punched it in anyways.  

The reason why I have a problem with this is, do people walk around and say "I can't write, or read". No their embarrassed.  I know this personally because I do have a hard time writing.  Words, grammar (as some may attest when reading this), punctuation and overall language is hard for me. But I don't say that it's okay for me to not be able to write.  I have done numerous writing course, read books on how to improve and I keep on writing (as bad as it may be). Why, because I know that it takes time and practise to become better.

This brings me to another conversation that I have had with a friend.  "Teachers don't teach math facts, so kids fail math."  He continued to say, " when I was in school we practised and practised and I knew them". You may ask how is this related, well if practising facts was all it took then this cashier would have remembered that 3 goes into five only once and that with two left over that is 2/3, which converts to .666666666. But did she, no, why because math facts or math In general doesn't happen in isolation.  Instead like any learning it happens in context and develops over time.

I am not saying that students should not learn facts but gone are the days of flash cards and mad minutes.  Practising facts should be done but through a way that promotes contextual use of numbers, much like how I solved it a moment ago.  Break numbers apart, play with them, change them to make sense.  Math is a beautiful thing and we often constrain our students to think that it has to be done a certain way or by a certain procedure.  Students need time to explore, build understanding and move along a continuum of understanding.

So as I end my rant, how do you teach math?  What strategies do you employ to help with facts? And how do you find a balance between content and context?  Love to hear your thoughts.

Friday, 6 December 2013

Being a connected Educator

Being a connected educator started for me one year ago.  It all started with a colleague of mine trying twitter for homework purposes.  I always wanted to try this and needed a push to do it.  This was my push and I am thankful for it.  Of course when I started out i just creeped a little, retweeted a couple of things and then started posting ideas and thoughts.  I finally found some great chats and learned a lot of that has changed many of my views on education.  However, it wasn't until this year and two experiences in particular that i would say I became a connected educator.

The first experience is meeting an amazing teacher.  Now when I say meet I mean online and through her posts.  I haven't actually met her in person, though I can't wait for that to happen (if it ever does).  The person I am referring to is Aviva Dunsinger @avivaloca.  By connecting to her blog and talking to her on twitter, emails and storify she has changed many of my views and thinking on teaching.  Because of her I have been more connected to my parents, learned more about inquiry and have struggled a little less in my transition to grade two from grade four.  Now some of you may say, how is this different from meeting great educators in person.  I would saying nothing; however, without twitter I would never have met Aviva.  We may never have talked and our paths may never have crossed.  This story is the same for many of the amazing people I have met on Twitter,who without it I never would have talked too.

My second experience is something that I am really proud about and has just recently happened.  It all started with a post from Angela Moses @Motechchef, another great educator.  She posted that she was having her kids rewrite the story of How the Grinch Stole Christmas from the Grinch's point of view.  I thought this was an amazing idea and so did another educator Carol McLaughlin.  Somehow after talking to the two of them we decided to collaborate together and have our three classes write the book together.  So even though we were separated by many kilometers (or miles) and time zones our classes were connected.  This would never have been possible without twitter. 

For this project Angela created a google doc to record our thinking.  You can also read her blog post here: You can also see our discussion here: http://t.co/VIAglPa2Vm.  Carol created a great graphic organizer to help the students understand the Grinch's feelings and I created a dropbox account for us to share pics and other things.

However, our learning hasn't stopped at making a story.  We have been posting pictures between classes.  Carol and my class have been blogging and I will be skyping  with Angela's class later next week.  The kids through twitter have been sharing their amazing ideas and have pushed each others thinking beyond the twenty or so in the classroom.  Not only this but they have been so engaged because of this collaboration.

So I ask you how have you been a connected educator?  Who do you think has helped you on your way?  Anyone that is great person to talk to, collaborate with or follow?

Saturday, 30 November 2013

Teaching through Inquiry or Problem Based Learning

I have recently been in many discussions with colleagues on teaching through inquiry that I thought I would put my thoughts into this blog. For me inquiry is everything.  I know some feel a more balanced approach is needed but in my opinion it is the way to teach.  The reason why I think this is that the students are engaged, it is there learning and through proper and impactful questions the students get a rounded program.  

What does teaching through inquiry involve?

The first is that it takes planning. Educators cannot expect to have a good inquiry, one that has meaningful learning, to happen just like that.  I have been encouraged by Mary Stein's five practise for planning a math inquiry (http://www.nctm.org/catalog/product.aspx?id=13953): anticipate, monitor, select, organize and debrief.  What these practise suggest is that we need to first anticipate students work, problems, strategies, and models.  This is where having a good understanding of curriculum, learning progressions and a trajectory of learning will assist in anticipation of student response. By anticipating, you can ask better questions, talk can be pushed and students will often move I learning because you can plan for it.  When educators are monitoring, they are constantly reflecting, thinking and questioning where students are, what they're learning and where the learning is going.  By monitoring you are also looking for student work to create the most impactful debrief that can happen.

The second thing is that inquiry needs a good context.  Students need to be truely engaged in the learning that they actually forget they are learning and are just trying to solve a problem. It is only the debrief that the learning goals become evident and brought out through careful questions.

Third, students need time. They need to have the time to explore, stubble, be in disequilibrium.  This is the hardest part for educators because we want to jump in and help by providing ways out. However, for the learning to have impact students need to be in that disequilibrium and be brought back and forth with careful but purposeful questions.

Finally, inquiry needs a debrief. Students need to have the learning brought back. Yes students will learn on their own, we all do this, it will just take time. As a teacher, educator we need to question, talk and bring the math or learning forward for the students to focus on.

Why teach through inquiry?

First students are really impacted by it. It becomes not just book knowledge but real learning.  Students also feel incharge of their learning. They are learning not just because you told them but because they want to learn. You cover more expectations and learning then you think and often with less review because learning is real and deeper.

How do you assess?

This is a question I get asked all the time.  Report cards, test scores, etc. are always at the forefront of education.  I personally think this needs to change.  What do we value more, learning or scores? In my opinion it's learning. For this to happen focus needs to be on descriptive feedback and formative assessment.  That being said I know we live in the real world and need marks. Through inquiry it is all there just in a different way.  Phasing a trajectory will help. It allows you to say to parents, administrator and colleagues, here is what research says, here is what we think, this is where they are and where they need to go. It is even more powerful then an a, b, or c. It gives students, parents and you the power to help and move students.

How do I get started?

Jump right in. Take so,e of your existing lessons and flip them. Instead of you guiding the learning or teaching the skills, have the students do it through a context rich problem.  There are also many resource: math: Cathy fosnot, Marilyn burns, john VanDeWalle, are just a few. Science: hands on science language: reading power series, rethinking schools, math that matters

Again these are just a few of my thoughts but there is a lot of research to back it up.  Inquiry is a lot of fun, it will surprise you. As I end this blog I would love to here what your experiences are? Have you tried inquiry? Problems? Questions? Thoughts?

Friday, 22 November 2013

Learning progressions or trajectories

Lately I have been reflecting on this word or really concept, learning trajectories or progressions. I first came upon the word when doing research for my thesis. We often have seen these before. Many teachers may be familiar with the ESL stages, first steps, Fosnot and Dolk's landscapes of learning, but yet when I say this word many of my colleagues kind of stare at me blankly as if I had two heads. This got me thinking, maybe I should just blog about it.

What are learning trajectories?

A learning trajectory is just want is said, a trajectory or pathway that students take to learning.  This pathway can take many different pathways and is often not linear.

Why is this important?

I think that as educators we have to consider learning trajectories in our planning and in our assessment.  They help us create questions and next steps. They also can help you plan mind on activities, problems for students to work with and help you anticipate problems that may arise in the lesson.  If your into Covey, it's really beginning with the end in mind.  It allows you as an educator to see the different pathways that students may take in reaching the end goal.

How do I use trajectories?

As I mentioned above, trajectories can be used for a variety of purposes.  I like to use them for three purposes:1) anticipation, 2) questioning, and 3) assessment, both for, as, and of learning.  

1) Anticipation: anticipation is an important part of planning and unit or lesson. It allows me to see where my students may have problems, which in turn lets me ask critical questions to move them along the trajectory. By understanding the stages of development I can see the possible potential learning for my students

2) questioning:  Questioning continues to be an important part of teaching. Often though, and I am guilty of this too, we find our selves asking questions just to reassure us that the learning is happening and not to promote further discussion or learning.  By having a trajectory we can ask critical questions in the moment. It allows us to see where a student is and where they possibly can go.  Without it we are more reactive to the students learning instead of being proactive. 

3) Assessment: by having a trajectory I have done my assessment. It is right in the trajectory. All of my learning goals laid out, all my next steps and big ideas. Everything is in a learning trajectory. Often I have one for each students and I make my notes right then and there, no need for rubrics, tests, checklists. A trajectory has all of this included.

How do we find them/ create them?

When I first started using trajectories for learning,me often used the ones that were already made, why reinvent the wheel if it's already done. But the more that I observed student learning the more that I saw how stud penny's developed learning.  To create it, just think about the most basic step or big idea that a student would use. Then think of the next step.  As you work through a problem make notes and the next time it will become easier.  If you really have time, read the research as it will help you.

As I mentioned above, there are many different learning trajectories out there. I know for math I often use the work of Fosnot and Dolk and their landscape of learning. John van de walle has many interesting trajectories in his book, elementary and middle school mathematics.

As I finish my thoughts here, just wonder how many of you use trajectories and if so for what purpose?

Thursday, 21 November 2013

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.

Friday, 15 November 2013

Unusual Animals

Thought I would share a great science project that we just completed. In grade two the students learn all about life cycles of animals and differnent animal groups. As a team we decided to give the classes a culminating task where they had to make their own animal.  Students had to first decide on an animal name, the describe what group the animal was from using the characteristics that we had been working on, then tell us it's habitat, and physical and behavioural adaptations.  Students then recorded their presentation using educreations and shared them with the world.  The kids were really engaged in this lesson and loved creating their own animal.  Here are some samples of the students work:

 

http://www.educreations.com/lesson/view/gurshan-s-unusual-animal/13186427/?s=UuyUv8&ref=link

 

http://www.educreations.com/lesson/view/gureet-s-unusual-animal/13183547/?s=fu7qdt&ref=link

 

http://www.educreations.com/lesson/view/pranav-s-unusual-animal/13177965/?s=4l4Z7u&ref=link

 

http://www.educreations.com/lesson/view/krish-s-unusual-animal/13176490/?s=VhbCaT&ref=link

 

http://www.educreations.com/lesson/view/navjot-s-unusual-animal/13127743/?s=VRUeF2&ref=link

 

http://www.educreations.com/lesson/view/manjot-s-unusual-animal/13113473/?s=VyE5ed&ref=link

 

http://www.educreations.com/lesson/view/avreet-s-unusual-animal/13113328/?s=vymFlX&ref=link

 

http://www.educreations.com/lesson/view/manveen/12972145/?s=7OYsVM&ref=link

 

http://www.educreations.com/lesson/view/sumaima-s-unusual-animal/13185979/?s=zeZrTs&ref=link

 

http://www.educreations.com/lesson/view/prabhnoor-s-unusual-animal/13180992/?s=zmdYtW&ref=link

Wednesday, 30 October 2013

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, 10, 313-340. 


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 LEAD the 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