Teaching through Inquiry

There has been a lot said about Inquiry in the classroom and you can take whatever side you want. However, for me it is such a fundamental component of any primary classroom.  This is because in my opinion when we are first learning a new skill it is through inquiry that we learn it. Very rarely is it through a lecture. In fact even as an adult when acquiring new skills do we do it through lectures but through mentor-ship and research.

For me teaching is all about the inquiry process. And teaching through inquiry allows you to meet all the minds in the classroom.

Now before I get too far in my post maybe I should articulate what I mean by inquiry, as I know there are many variations of the process out there.

Throughout my teaching career my journey through inquiry has undergone a lot of changes. When I first started teaching I thought what I did was inquiry. I would plan lessons that were hands-on, engaging, thought provoking and had plenty of talk built in. Students would often be engaged with problems, experiments or activities that required them to think, problem solve and then discuss.  Now I know many of you are thinking but isn’t that inquiry and you are correct.

According to Google, inquiry is:

in·quir·y
ˈinkwərē,inˈkwī(ə)rē/
noun
  1. an act of asking for information.

However, what I was realizing was that I was the one doing the inquiring. I was the one that set the stage for student learning, I was the one that debriefed and discussed the learning.  I felt that this type if inquiry was more about me and less about the students. So I changed. I changed my thinking to be more student driven. My units often start with provocations, which then lead to questions, which then in turn lead to students recommending further learning. I still insert my thoughts but now they are developed through asking questions and using student talk to deliver the observations and learning.

Now why do I love inquiry so much:

The first is that I love it engages the students in the learning. They feel situated and invested. They want to learn because they like to learn. I even have students going home and asking their parents to go to the library or go and research because they want to find more things out about the topic they learn in school. I don’t know about you but this is truly amazing to hear.

Second through inquiry you really understand the nature of your students learning. Because I am not lecturing and then asking students to complete a test where they regurgitate the information I just spewed out at them they have to rely on their own thinking and schemas. You also get to question them and conference more on a regular bases and because of this you see their growth and understanding. Assessment is a breeze because you have almost too many observations and conversations to choose from.

Finally, I look at this world around us and I think that the jobs I am preparing my students for don’t even exist yet. Now you are right some jobs will exist put for the most part the skills that these students need will not. However, what will is the ability to problem-solve, be adaptable, creative, and flexible thinkers.

I recently came upon this:


I love the fact that the first three skills are soft skills, one that you really cannot learn from reading a textbook or listening to someone tell you things. They are skills that take time to develop and through multiple experiences and situations. In my opinion inquiry does this. 
Now these are just my opinions but ones that have been grounded in my practise. They are observations of my growth and reflection. Would love to hear your thoughts?
What do you think of inquiry?
Do you like it? If so why?
What are the benefits? Drawbacks?
I would love to hear your opinions.
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A Reflection on Assessment

In a couple of days I will be presenting at Bit14 with Aviva Dunsiger. Our presentation is bridging the divide: Opening our four walls. However, I digress from my blog title. The reason why I am writing this is because I was also asked to co-facilitate a discussion with Brian Aspinall on assessment in a changing 21st century learning. This is going to happen on Thursday at 10:00 in the learning commons.  It is a free forming discussion but I thought I would get the ball rolling with some of my own thoughts and more importantly questions.

First of all with our assessment document in Ontario (Growing Success) there is a big emphasis on assessment for learning, as learning and of learning; with a large focus on assessment as learning and for learning. This is a big shift for many of us teachers who before this did a lot of assessment of learning. Not to say that this isn’t important but that there has been a big shift in thinking about assessment.  This shift also aligns strangely enough with a wider acceptance on qualitative data versus quantitative data.  That observations and discussion are just as valid and important as the number that we can collect.  Which brings me to the reason for our learning commons discussion.

The discussion came about when Brian made a post about a brand new app call Photomath. Basically its an app that can do algebraic equations for you. The question that Brian raises is what are we assessing when an app can do the math for us? Should we be assessing basic skills like this?

My response to this was there needs to be a shift to not what is the answer but how do you know the answer is correct. It reminded me of the calculator debate when I was in school. I still remember this movie we had to watch in grade eight and the two children were adding up some money. One of the girls takes out a calculator and clearly gets the wrong answer but strongly argues that she is right. When asked why, she states because the calculator told me. It turns out that the calculator was running low on batteries and if you used basic common sense then you would have known the answer was wrong. The point wasn’t so much that she got it wrong but that there was faith in the answer because the technology told her so. The problem is that students then and now need to have a good conceptual understanding of the work before jumping into abstract thinking. They need to understand the process in learning.

The world has changed a lot since we were in school, heck even since I was in school (which to be fair was not that long ago). If you honestly look back and think about those school days, the information that we were given potentially would have lasted us our life time. To be fair the information our parents were taught did last them their lifetime. However, that is not so with the kids we are teaching. Technology has changed the way we use, process and understand the world around us. We live in a world were tomorrow has endless possibilities. The scary part is that I am preparing kids for a future with obsolete information and knowledge.  Which is why philosophies on assessment have drastically changed.

A couple of years ago I was giving a test to my students. I looked up and saw that my students went right to talking with their math partners, trying to solve the questions. I was about to stop them and state that this is a test I need to know what you know when I realized that I already knew what they knew. Because of teaching in a constructivist approach, I knew where they were struggling, what strategies they would answer, and how they would communicate. In fact I knew why certain students were talking and asking questions and I knew what next steps would be useful for them. This test wouldn’t tell me this, in fact it was wasting two hours of time that I could be conferencing with my students and helping them move forward.

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Students collaboratively working on creating success criteria for an assignment

Now I said I knew a lot, why?  The reason is that in my teaching I am always conferencing with students, individually, and in groups. I have honest conversations with them and ask them questions to test their knowledge. Based on their responses and work samples I am able to see where fit on a continuum of learning. In fact I can confidently say that I understand my students more from this method then I do with a summative assessment like a test that I would have traditionally given. Not only that but my students move faster up that continuum because of our conferences and reflections that are done everyday versus just studying for one test to then forget about it the next day.

For me it is more important to teach my students to be curators or data, critical thinkers, problem solvers and have creative/adaptable thinking skills.  I say this because the information I am teaching them will soon be obsolete.  Now please don’t get me wrong and say that students don’t need to have basic skills or test taking abilities. Unfortunately in this school system and society they still need those test taking skills and yes students do need to learn basic skills (arithmetic, writing, reading, etc.) but the emphasis shouldn’t be on memorizing to retain for an hour but to go deeper with that thinking and be able to understand why we are using it not just knowing and forgetting.  

This brings me to my questions and ones that I hope everyone help can answer:

1) What assessment tools do you prefer and use in the classroom?

2) What skills are needed, as a teacher, to make assessment as and for learning effective for growing student achievement?

3) What do you think about the shift in assessment? Is it warranted? needed?

4) If we are moving to a more assessment as and for learning, how to we do this?

5) What is the biggest resistance to this change? How do we over come it?

I am really excited for this conversation as I think we are on the brink of exciting change in education. Would love to hear your comments and ideas about this topic, no matter what they are.

Why do we Need to Argue over Math? –> A Call for a Balanced Approach

About a month ago a colleague of mine Kyle Pearce wrote a post “Does memorizing multiplication facts hurt more than help.” It was a very interesting read and I happen to agree with Kyle’s point of view.  As many of my frequent readers of this blog know, I prescribe to the constructivist approach to learning mathematics.  I believe that students through discovery and proper guidance will be able to understand a wide load of big ideas and theories.  Not only do I believe this but I have witnessed this first hand with my students in every grade that I have taught.

However, this is not so for many people.  In fact it was a discussion on Kyle’s blog post (feel free to read the thread) that has me thinking more and more about this topic. And not only thinking about it but trying to fix and insight thoughtful discussion around the ways in which we are teaching math.

Maybe a little background first.  Math has been a hot topic for the past year, if not for the last century.  For many countries, provinces, and states, math curriculum has undergone a significant change from what we grew up with as children.  Some. like myself, believe that these changes are for the better, some have not.  I was recently at the OAME and listening to Brent Davis a professor at University of Calgary.  In his lecture he shared that the reason math curriculum was introduced was so we could have a work force to crunch numbers, nothing more and nothing less.  As we have evolved beyond that (not saying fact crunching is not important) our skills have also changed and I think this is what we need to remember; we have evolved.

For this reason I and many others are proposing a  more balanced approach to mathematics.  Lets stop this war and needless debates and get to teaching good mathematical practises.  One in which our students will push their thinking and really think about the numbers.

If it was up to me this is what I would include:

1) Math should be linked to Big Mathematical Ideas:

I think this is the first step to thinking about our students as mathematicians.  Catherine Fosnot (2002) has some very interesting work around making our students mathematicians.  One of the most interesting facts is there was a study done with so many mathematicians and they were asked to solve a problem.  Not one of those mathematicians solved it the same way.  I found this interesting because that is what I see math.  Math is about the mathematics and there is not one way of doing things.  We have to teach our students the understanding, the flexibility and the patience to be mathematicians.

2) Math is about real numbers:

Students need authentic experiences to learn.  Let’s think about ourselves and how we learn.  Now some do learn through reading and replication but if you honestly think about how you learn a concept the best; it is through trail and error and than guidance from a mentor.  This is the same for our students.  They need real experiences so that they can play and discover the mathematical concepts.  In my personal experience both in tutoring high school students and teaching mathematics in the primary and junior divisions it’s the contexts that allow students to really understand what they are doing.  It’s the context that helps them build models of representation.  In my classroom, these are often done through social justice problems and real life contexts.

3) Students need time to explore:

This goes hand in hand with the above comment. As much as we need instruction, we also need exploration. Students need time to make mistakes, reflect, debate and discuss. These experiences allow students to make connections between concrete and abstract thinking. I was reminded at the OAME that every mistake makes a new synapse in the brain. We need these mistakes I order to solidify  our learning.

4) Students need Mentors:

My most recent research in understanding teachers questions has shown me the importance of teachers, not that I didn’t believe that before.  With a shift towards discovery learning, we as educators have forgotten the importance of our role, or what even our role is.  I truly believe that we should not be the dispenser of knowledge but the mentor of that knowledge.  Though through exploration students will learn (many studies to show this) they may not have tools to reflect or pull together the big ideas.  I think this is where much of the back lash has come from discovery math, reform math or whatever you want to call it.  As students explore and discover there needs to be some sort of guidance.  This is where a teacher can shine and help students with the mathematics.  However, my research shows that for this to happen, a teacher needs to 1) have a good understanding of mathematics, 2) have a good understanding of how children learn mathematics and 3) plan. I know that all teachers plan but this planning involves thinking of big ideas, landscapes and possible questions.  It is these questions carefully placed that can allow students to figure out and make mathematical connections.
Take a look at this video of three of my students thinking about fractions.

They have never been taught fractions from me before this and in fact as a class we haven’t even started the unit. However, that being said think about their learning and the role they play and the role that I play as a teacher.  Where do my questions come from? Why did I ask them at the time I did?

5) Time for debating, conjecturing, discussing and proving:
For me this is the time for a teacher to shine; however not in the traditional sense of standing in front of the class and lecture or tell students how it should be done. Just like students need time to explore they also need time to debate as a community. It is through this debate that students defend their thinking, conjecture, question and solidify their learning. Moreover, it goes beyond just showing and telling.  As a teacher the types of strategies that you show matter. How are you building the learning up, what questions are you modeling? How are you focusing the talk? How are you fostering talk? These are all questions that a teacher needs to be asking.
Also take a look at my most recent grade two conversation of multiplication.

6) Repeated Practise:

Yes I said repeated practice! Students need it, but it’s not just doing procedural learning over and over again.  When I say repeated practise I mean a similar problem for students to continue their exploration.  Students, well most students, cannot solidify their learning through one experience.  In a typical unit my students will solve about 7-8 problems that could take three to four weeks to learn.  These problems build their learning and knowledge from day to day.

7) Skills:

Yes skills are important. They are needed but they are not needed like we use to think about it. For me it’s how are we introducing facts. Do we make students think through facts? Are they taught in isolation or allong with concepts?  In my classroom, students practise facts at home, they play math games in the classroom (here is a file of my math games:  https://drive.google.com/folderview?id=0B4245QONE7HaaHl3M3ZKNWd3SUk&usp=drive_web). In addition before my problems start I often use string lessons which builds on mental math strategies and learning how to be flexible thinkers and playing with numbers. This to me is more important then struck memorization. It teaches students that numbers are not confined facts but that you can pull apart numbers and use known facts to solve other facts. Through this process students often learn all of their math facts, can recall them and use them in problems, which to me is way more important.
These are just a few of my thoughts on what I am calling a balanced math approach. I have a few more  to hash out around integrating and  implementing a center approach within my problem solving approach.

What are your thoughts?  Don’t you think it is better to discuss and fix our problems rather than lay blame about which is better?  Shouldn’t we think about our students first and their needs in their 21st century world?  Love to here your thoughts.