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.

Helping students Master Facts

Coming from Junior grades I know that facts are important for students to help them with math.  In addition, I know that learning facts also helps students with solving problems.  However, whenever you talk to anyone this is such a bone of contention.  Some feel that facts are the most important parts of math and some feel they will be learned through problem solving and inquiry.  I tend to lie in the middle of these groups leaning moreso to the inquiry approach.  Don't get me wrong facts are very important to learn and are a critical part of mathematics.  They do help students; however, I also see the other part where students only know facts and cannot apply them to problems.  IN this case facts are harmful to students development because they keep trying to apply rote learning with no understanding.

So with this in mind what is a teacher to do?  I recently came upon some great advice from van De walle's book, Elementary and Middle School Mathematics: Teaching Developmentally.  In his book he has a whole chapter on mastering basic facts.  Van de Walle offers three components to learning facts and none are through strict drill and or quantity of drilling facts.

His components are:

1) Help children develop a strong understanding of the operations and of number relations.


2) Develop efficient strategies for fact retrieval

3) provide practise in the use and selection of those strategies

This is great but what does this look like in a classroom.  I can't say for others but in my classroom this is how I have interpreted these components.

Number sense is beyond just learning algorithms or memorized facts.  You need to understand how numbers work together, their significance, decomposing and composing, and other mathematical reasoning.  All of these help you with mental facts, which in turn helps you with mastering basic facts.  In my classroom, we do a variety of things:
                              
                       a) String lessons: this is fifteen minutes before the problem where we practise mental facts.  These strategies relate to the problem and I hope that students start to apply them in the problem.  This might be adding by tens, using friendly numbers, adding with doubles, etc.

                      b) Problem Solving: chosing a proper problem is just as important to helping students learn math facts.  The problem you chose should allow students to practise their fact recall and not just a traditional algorithm.  In addition, when you debrief the problem there should be some talk about efficiency and using these facts.  This will promote student thinking in this area and see why its important to learn and use their facts.                       

                      c) Teacher Talk: Often when students talk about a strategy I will articulate with certain math talk.  So what you are telling me is this.... Your use of vocabulary will always assist student learning.  I also sometimes do think alouds of my thinking, to help student conversations.  This always is accompanied with talk about what students think I did.

                         b) Math games that focus on these skills.  All of our games in the classroom focus on certain skills.  It helps students practise their facts and learn about numbers beyond just pure memorization.  It also brings out talk among students and teacher.

In addition to this we also do math fact Mondays and Math game Friday.  During Monday my students do a "mad Minute" type of activity.  Though it is not truly a mad minute as it is more about practice of facts then of fast recall.  Students do have a time limit but it is more that it happens at the end of the day.  I will also like to say that my students asked for this activity and relish the moment when they can show me how much they have learned from the week before.  I give my students ten minutes to answer about 60 questions.  We also graph our results over the weeks and set goals for the next.  The emphasis is on goal setting and improving their individual learning.  Results are never shared among the students.  On Friday we do a whole period on math games.  This is important as it give students time to play and practise.  Even though that after finishing a problem they do get to play games not every child gets the same amount of time, this way they do.

Furthermore, Van deWalles chapter there are many great suggestions on the type of strategies that these things can bring out and is a read I recommend all teachers doing.

This only some of the things that I do in the classroom to assist in fact recall.  It is important but how you do facts is just as important.  How do you help with facts?  What type of activities do you use?  Love to here from you.

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.

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.