What's Wrong With How We Are Teaching Math?

Ontario needs to improve teacher training in math, the province’s Education Minister has said in response to standardized test results that revealed students are losing ground in the subject for the fifth year in a row.

CAROLINE ALPHONSO AND ADRIAN MORROW
The Globe and Mail
Published Wednesday, Aug. 28 2013, 11:31 AM EDT

It seems all eyes are focused on Junior Math in our schools this Fall.  Everyone is asking, why are our scores dropping in Math?

For the last several years, the Education Ministry has been encouraging teachers to teach Math through problem-solving using a three-part lesson.  This mandate is grounded in research.  In our board, like many others, our Elementary teachers have been involved in the CIL-M (Collaborative Inquiry and Learning in Math) meaning they have been learning together, through a co-planning, co-teaching, debriefing model to learn how to teach Math through-problem solving using a 3-part lesson.

So why have the scores been dropping?  Over and over again I hear teachers saying "So, when are we going to admit that the 3-part lesson doesn't work?" And I hear parents saying "Teachers need to go back to teaching the basics.  They need to teach Math the way I was taught."

Are they right?  I've been thinking about this question a lot lately, and I have to say "NO!"  The 3-part lesson and teaching through problem-solving WORKS and it is the best method for helping students to develop deep conceptual understanding of mathematical ideas.  So, if I am right, why haven't we seen the scores improve in Junior Math on our EQAO Assessments?

I have several theories that might explain why the scores are not improving.  I believe that our lack of improvement is actually the result of several factors.

1.  Teachers have not fully bought into the 3-part lesson and teaching through problem-solving

• What I have noticed during many of our co-teaching sessions is that teachers have a really difficult time "giving up the floor". The first part of the 3-part lesson, which should be a 15 minute introduction or "Minds On" tends to go on for closer to a half hour of straight teacher talk. This is because old habits are difficult to break and teachers don't fully trust that the learning should and will come out during the third part of the lesson, the Consolidation.  They feel that they have to provide students with enough information at the beginning of the lesson for them to be successful in solving the problem during the "Action" portion of the lesson.  They run out of time in their lesson, and the Consolidation ends up being only 5 minutes long, if it takes place at all.  So while on paper, the plan looks like a 3-part lesson, what is happening in the classroom is much closer to traditional teaching.
• Some teachers see the 3-part lesson and teaching through problem-solving as a "Friday" activity and teach traditional methods during the rest of the week.
• Teachers did not choose to be a part of the CIL-M, they were told to be a part of it.  I've asked many people to explain what their "inquiry" in Math is about and they don't even seem to know that they are inquiring about anything. I've also asked "What is the goal of your PD session today?" I've yet to meet a teacher who is a part of the CIL-M who can answer that question.  They are attending as a form of compliance not because they are hoping to learn something new.  Just like our students can be compliant with a learning task without knowing or understanding the learning goal, so can our teachers!

2. In order for teaching through problem-solving to work effectively, teachers have to be excellent at formative assessment

• In order for teaching through-problem solving to work, the problems have to be in a student's zone of proximal development.  This can only happen if the teacher has good assessment for learning practices and knows exactly what his/her students are ready to learn next.  The teacher has to differentiate for students at different places on the Math learning continuum.  
• Teachers need to be able to determine, through assessment and making learning visible, what students misconceptions are so that they can address them.  This leads to very tailored, explicit instruction, but again, requires that the teacher is an expert at formative assessment practices. 

3. Teachers have to themselves have an excellent understanding of the Math Curriculum 

• Many of our teachers lack confidence in teaching Math.  They don't consider themselves experts in Math, and struggle to identify the "Big Ideas".  Teachers today were taught Math by traditional methods; many of them only have rote learning of mathematical algorithms, and don't have deep understanding of mathematical concepts.  Here is a small example of what I mean: how would you compare 6/7 to 7/8?  When I ask teachers this question, they automatically begin to create equivalent fractions using common denominators.  That's because they don't truly understand fractions.  They should be able to see that each fraction is one piece away from a whole, and the eighths are smaller pieces than the sevenths so 7/8 is the larger fraction.  

So what do we need to do about this?  Well we need to acknowledge that we have a problem of practice.  And saying that we are going to teach Math through problem solving isn't going to truly address that problem.  We need to dig deeper, be more specific.  What do we have to change about our teaching practice to address this learning deficit in Math?

I think we need to do the following:

• We need to assess our students' mathematical understandings BEFORE we begin a unit of study, but we also need to assess them along the way to determine if we are having an impact.  We need to be responsive to our students' needs.  In order to do this effectively, teachers need to develop their formative assessment strategies.  I like Dylan Wiliam's Embedded Formative Assessment and our Ministry's AER Gains site for professional development on formative assessment.
• We need to develop our questioning strategies to provoke thinking, elicit misconceptions, and scaffold student learning to address misconceptions
• We need to use rich multi-step problems that are open-ended or have multiple paths to a solution; that way students have multiple entry points. Dr. Marian Small's resources help teachers to develop rich problems that address the Big Ideas and common misunderstandings that students have.  Here's a PDF that shares Marian's teaching strategies for focusing on the Big Ideas in Math through open tasks. 
• We need to explicitly teach accountable talk in the Math classroom using prompts to promote student-to-student discourse and discussion. Cathy Marks Krpan's Math Expressions is a great resource to help teachers develop student thinking and problem solving through communication. 
• We need to make Math concrete.  Students can't understand the abstract until they understand the concrete.  We have to stop saying,"Here are the manipulatives if you need them." No student wants to say they need something others don't.  We need to say, "Use these manipulatives to prove your solution." Students who are using an algorithm but don't have conceptual understanding will be forced to explore what the concepts really mean. 

Teachers can learn along with their students, but they can also learn with their colleagues through a co-plan, co-teach and debrief model.  Teachers need to get together to look at curriculum expectations along side their student needs before they develop problems.  Once they know what their students need to learn, together they can develop rich problems or activities for their students.  They need to moderate student work together to establish what they now know about what each student knows and can do, and where each student needs to go next in order to achieve the learning goals.   We need to be intentional in everything that we do!

But most importantly, teachers need to recognize that every classroom is a laboratory, and every lesson is an experiment.  We formulate a hypothesis, "if I teach this concept this way, the children will be able to ...." and like any good scientist, we need to observe the reaction; what are students doing?  What are students saying?  Then we judge the evidence.  Were we effective?  What impact did we have on student learning? If we're not effective, we have to create a new hypothesis and determine how to fine tune our teaching to meet the needs of the students in front of us.  

Making Shift Happen - A Time For Reflection

It is July once again; a time for reflection.

This past year has been the best year I have ever experienced in my teaching career. This is due in large part to the learning that I have experienced this year and the teaching networks I have been a part of. I am more aware than ever that while we are often the only adult in our classroom, teaching is not by any means a solo pursuit, it is meant to be something that is done in community.

The entire paradigm of teaching has shifted. No longer is a teacher the impart-er of knowledge and information; a teacher is now a role model for learning. More than ever this year, I developed a learning stance, and became the chief learner in my classroom, and that made the year fun and exciting for me, and learning a contagion for my students.

Creating strong learning networks that I could go to for advice and ideas was really important to me this year. I am so grateful to all of the very excellent Grade Six teachers in our board that lent me their ears!  I am also grateful to my friends in other boards who acted as objective listeners to my sometimes fantastical ideas. And lastly, I'm extremely grateful to all of the incredible educators I have met in my virtual network via Twitter, Google+ and ETMOOC.

Today I started tutoring a 12 year old boy in Math.  I asked first to look at his report card, and saw that he averaged about a 67% in most subjects. In the Learning Skills section, I noticed that it was stated he needed improvement in "Self-regulation" and "Independent work". I pointed this out to him and asked if he has trouble focusing and paying attention.  He said "Not really". I said "is your class rowdy and do the students fool around a lot?" He said "Pretty much". I asked him to describe a typical Math lesson. He described a class where the teacher taught the lesson at the front of the room for the first half hour, then assigned the questions in the text book for the second half of the period. He mostly ignored the lesson and the questions while he socialized with his friends.

I asked what part of Math he found most difficult, he didn't even hesitate before answering "percentages". I asked him to complete a Proportional Reasoning Diagnostic from our Ministry's Closing the Gap on the Math Gains website. It was apparent he didn't understand the relationship between fractions, decimals, percentages, rates and ratios. We started with factors and multiples, quickly moved to numerators and denominators, then equivalent fractions. I was amazed at how quickly he caught on.  Within one hour he was solving rate problems by converting to a unit rate.  So why didn't he learn all of this in school?

It is no longer okay to teach the way we were taught!  For so many of our students, (I would argue especially our boys), it just DOESN'T WORK!

Although I've had an excellent year in the classroom, and am well aware that I still have so much more to learn, I am leaving the classroom for a temporary hiatus to go back to the Curriculum Department. Hence the name change of my blog! I am going to attempt to Make Shift Happen! We classroom teachers need to change the way we are teaching so that we reach the students most at risk in our classrooms. Every child has a right to succeed and it is our duty to make sure that that happens. I'm hoping that I can support teachers in making that shift happen in their classrooms.

I'm scared though, scared because I know how teachers feel about enforced PD and enforced "Professional Learning Communities". My blog post and the comments that ensued on the PLC vs the PLN (Professional Learning Network) were an eye-opener for me. My challenge this year will be to find a way to be a co-learner with my fellow teachers and support them in making shift happen. I am really hopeful that I can inspire and motivate my colleagues the way I have been inspired and motivated by my PLN. I think the key elements are voice and choice, I just don't know yet how to ensure those elements are embedded in my work with teachers.

I will once again welcome your ideas and opinions. Your comments and emails will be more important than ever to me on this portion of my learning journey.

Using Social Media to Differentiate

I've been feeling guilty - all of my favourite teacher bloggers have been taking advantage of their time off and have been updating their blogs.  I've had a hard time getting off the couch!  On Christmas Eve I came down with a strep throat and am just starting to feel like myself today.  Since I've had nothing to do but lie around, I have been enjoying all of those blog posts!

One such post was by Royan Lee "The Power of Introverts~ Spicy Links."  Royan shared on his blog Susan Cain's TED talk "The Power of Introverts" along with links to his interview with her on her website.  Susan also has her new book out now - "Quiet: The Power of Introverts".

As we all know, one of the hallmarks of 21st Century Learning is collaboration.  Cooperative learning is everywhere.  Students collaborate on projects, discuss texts they've read to hash out meaning, co-write text, peer-edit, etc.  Susan Cain reminds us that it is not always the loudest or most vocal, however, that has the best ideas.  Most teachers realize this, and we often torture (and I don't think "torture" is an exaggeration) our introverted students begging them to share their ideas, because we know the rest of the class would benefit from their insight.  (Then we give them a level 2 for Oral Communication- which if we really were evaluating based on the Curriculum expectations we'd realize that Oral Communication is so much more than being able to speak publicly- but I digress.)

Royan's answer to this issue is Social Media. (I've been following his blog since I saw Lisa Donahue at Reading for the Love of It last February, and she mentioned him- one of the best things I ever did for my teaching practice!)

I found out how right Royan is when I began using Blended Learning this year.  Blended Learning incorporates a combination of face-to-face with on-line instruction.  We use the Ministry's Learning Management System the Desire 2 Learn (D2L).  Using the D2L has allowed me to use "Office Hours"- time when my students can contact me via the D2L outside of the regular school day.  Most of my students have taken advantage of this feature, but I find it is my shy students who use this feature most regularly.  One student explained that she has "so many questions" but is uncomfortable asking them out loud in class.  The D2L makes it easy for her to ask questions.

We have also been using the Discussion tool.  This tool has given those quiet thoughtful students an equal opportunity to have their voices heard.  Introverted students often like to think before they speak.  The fast pace of a group discussion doesn't allow for that.  They also aren't pushy enough to interrupt those extroverted students who know exactly how to have their voices heard.  Using the Discussion tool solves both of these issues - they can take as much time as they need to think before they "speak" and everyone has to "hear" them.

Social Media allows us to use cooperative learning while still considering the individual needs of our students. For some of my students, having to "write" their ideas into a Discussion Forum is painful; writing ANYTHING is painful.  The Discussion Forum on the D2L also allows students to compose their messages as an audio file.  Now that is differentiation!

I'm going to order my copy of Susan Cain's book today!