Friday, February 5, 2016

Creating Discourse-Friendly Classrooms

Some great simple things to create a discourse-friendly classroom from
"Literacy Strategies for Improving Mathematics Instruction" (2005)

  • Arrange desks so that students can easily turn to see each other.
  • Encourage students to direct questions and explanations to the class, rather than the teacher.
  • When recording ideas, use the students' words as much as possible.
  • Try not to repeat or paraphrase everything students say.  This teaches the other students that they can simply listen to you.  Ask the student to repeat louder if need be.
  • Remind students that a conversation has both listening and speaking skills.
  • Stand in a variety of spots in the classroom.
  • Remember, students listen harder when a peer speaks than when an adult does!
  • Give students time to think.
  • Arrange lessons so that students have a product to share as they explain their thinking.  
Even better is if the student takes the lead in the class.  This is done by 
  • Asking open questions to stimulate thinking.  "Is this logical?" "What do you wonder about?"
  • Honor ideas even if they are incorrect.
  • Encourage arguments between students.
  • Confusion is ok!  Make sure students know that you want them to be confused, and that you will let them be this way.
  • Tangents are great teachable moments.
  • When a student brings up an idea ask the rest of the class if they have any questions or ideas.
  • Counter questions with questions not explanations. 
  • Even with a correct answer, ask if there is any another way this can be done, or if there are improvements to be made.
A great reminder!

Thursday, February 4, 2016

Math wars confusing curriculum and pedagogy

Recently, in the media there has been a lot of false statements around the WNCP curriculum, and consequently these attacks fall on the hands of teachers.  Before I continue I will explain two important words in the educational world.

Curriculum: This is simply WHAT a teacher needs to teach.  For example, a Grade 3 student needs to be able to recall and understand up to 5 x 5.

Pedagogy: Is HOW the teacher teaches.  For example, using direct instruction, peer coaching, PBL, etc.

Contrary to social media, presentations, and other means of critiquing the curriculum, the curriculum does not say:
  • How teachers need to teach the outcomes.
  • Discovery learning is a must. In fact the word discovery does not appear once in the entire document.
  • "21st Century skills development", and "experiential learning".  Neither of these phrases appear once in the entire document.
  • Students should not be memorizing their basic facts.
Keep in mind that the curriculum is the WHAT not the HOW nor even the WITH WHAT.

Recently, an event, around public education, was held in Calgary at a private, gated school. The event was designed to inform parents of "the best practices in math".  While the event was designed to encourage change at the government level, make no mistake this was a blatant attack on math teachers in Alberta, and other teachers in provinces following the same curriculum.

 Here is one of their recommendations:

Now as you can see "Teaching Strategy" does not fall under curriculum but actually pedagogy.  The irony is that I am sure all teachers, at some point, do some direct instruction.  I have had the honor of being in many math classrooms around the province and I can attest that teachers have balance.  This slide almost paints the picture that teachers are simply sitting around hoping that students will learn math through osmosis.   Also, there is no "imposing of one model of instruction".  Enter a classroom and you will see that teachers truly implement strategies which are the most beneficial based on the classroom make-up and the outcome(s) being taught.

Next we have "Some things to watch out for"

Of course some of these points make sense.  We should be wary of many phrases as their intent could be misguided. Also, in reference to the second point, no one is arguing against memorization and procedures.

For their third point, I have not met one person who suggests that students should not memorize their math facts. The difference is, however, students should memorize these facts out of application and use, not out of necessity.

This means, show students math in a context and for a purpose, and the memorization will occur.  Have students roll dice, play cards, board games, car games, etc, as most (if not all) games have some link to reasoning, logical thinking, and mental mathematics.

"Understanding is not more important than skill"- This is again in reference to the actual art of teaching in the classroom.   I have yet to meet one teacher who denies that skill is useful, but let's remember if we only focus on skill then learning can be disguised with simple memorization.

So why is there such an attack on the curriculum?

I believe because some are confusing the terms curriculum and pedagogy.   Also, because we have a generation (parents) who learned math through memorizing algorithms and are confused around why their own children are not coming home with the same algorithms. Recently, some parents are now seeing the benefit of the change.

Also there has been use of the drop in PISA scores, however there has been no actual evidence that this drop has been caused by curricular changes.

The confusion, for a child, might start when a child is learning one way at school, and then coming home to hear that the strategy is not right.  We must also realize that teachers are trained professionals around education.  These professionals implement effective instruction based on the individual needs of the students.  It is unfortunate that some want to see the art of teaching go to a procedural task of "tell students what to do, ask students to imitate the learning, repeat".

If you have a question around the math your child is learning, phone the teacher.  Social media, news, and other hands not in K-12 education, have a way of distorting the truth.  Keep in mind that teachers are trained to teach your child math in a way that is meaningful, and creating a passion towards numbers.

I remember back when I was in school and how there was an immense number of people whom hated math.  It seemed as if math was the number one hated subject in school. (No research simply guessing here).  Isn't it time this changes?  Isn't it time we cultivate passion and number sense?

Math class needed a change, and this change is healthy.  There is now balance.  Before it was taught one way and all students were required to learn that one way,  and now alternative efficient strategies are not only accepted but encouraged!  We are allowing students to not only learn math, but actually like it!

Wednesday, February 3, 2016

When is the world going to be full?

A possible project which could be used in a math class.  I have designed this to fit in the Alberta Math 30-2 curriculum.  Feel free to change or alter as you see fit.

Pose the question:

Introduction: When is the world going to be full?
Give students 5 minutes to talk in groups.  After, have a debrief and share possible hypotheses.

Next, ask for possible information we will need to answer this question more accurately.  Some other possible questions might be

  • How many people can fit on the plant?
  • How many people can the plant sustain? (Different question than the first)
  • What is our current growth rate?
  • What is our current population?
Some of these questions will be easy to solve, while others might be more difficult.  I would ask students, in groups, to research the answers to the questions they asked.  Some of these will have an answer all will agree with, such as "What is our current population?", while other questions might have a range of answers depending on the website found, such as "How many people can the planet sustain?"  Create answers that everyone in the class can agree with, or even commons answers in different groups as long as each student in each group agrees.

Creating an extrapolation of our population.

You can google our current growth rate, however this number, most likely, has no meaning or even understanding of how it was derived.  As a class, possible growth rates will be explored.  Below is a chart of recent population numbers on our planet.  (You might want to use different years, or more years).

Population (Billion)

Now the question becomes, "What sort of data is this?"  This is when I would pause and teach exponential, sinusoidal, linear, quadratic, cubic, and logarithmic functions.  Using this data, I would create an equation of each type of function.  Here is a graph of all the functions displayed together...(I used 1970 as year 0.  This occurred as, after deciding this, I needed more data points. I also added a logistic curve to show what would happen if population growth become 0)

Now is the discussion time.....

Ask some general questions such as:
  • Any general thoughts?
  • Any similarities?
  • Could you create a possible scenario in which each graph would be accurate?
You could also embed the critical learning of each function into this:  For example you could ask:
  • What is the amplitude, period, and median value for the sine function?  What does that mean in this context?
  • What are the zeros of the cubic function, what does this mean in this context?
  • What is the growth rate of the exponential function?  What does this mean in this context?
And any other questions which may come to mind.  Now you may want to remove any functions in which the class agrees might be inaccurate.  Such as the cubic, sinusoidal, and/or linear.

Using the remaining graphs determine when the Earth would be full, using the number the class researched earlier.  The answers might be earlier, or later, than the class first hypothesized.  

Have the discussion "Should population growth be addressed? Why or why not?"

Do not rush this project, take your time.  Stop, throughout, to teach certain skills, or concepts.  Also allow students to research on their own and pose their own questions throughout.   

Tuesday, February 2, 2016

Math as a language

If math is a language then we need to treat it as such and the best way to learn a second language is immersion.

Focusing on math in grades 1-6, children, when they come home, should be speaking this language.  Parents should ask their children what "words" they are learning.  These "words" could literally be English words such as "prime, composite, factor, multiplication" or it could be what Schwartz and Kenney, 1995, suggest are mathematical nouns such as numbers, measurements, shapes, spaces, functions, patterns, data, and arrangements.

Next, as a language it is important to learn it in a context.  Imagine if I asked you to conjugate verbs and nouns of a language through worksheets and repetition, how much of this practice would stick?  This is similar to children learning "naked numbers"; sitting and simply reciting their times tables.   Suppose there was one child learning math through flash cards and forced to recite their multiplication tables, while a second child plays board and dice games, counting activities while you shop, or even helps you count your change at the grocery store. Which child's experience would "stick" more?  Which child would grow to enjoy numbers and which would grow to hate it?

Keep in mind that the way a child learns a new concept is extremely important in how effective the learning truly is.

One common technique to learning math is through mnemonics or jingles.  However, I want to relate this back to learning a language.  I can sing the "Canadian National anthem" and "Happy Birthday" both in French due to the nature of how I learned it; through the song and rhyme.   Other than these two songs and some simple phrases, I remember nothing else in French.  Do I understand French?

Learning, or essentially memorizing, through jingles without connection to deeper meaning will not allow the child to retain the understanding needed to store this knowledge in their long term memory and ultimately not allow the child to extend this thinking for a new purpose later on.  (I can think of many multiplication songs, which don't really teach the idea of multiplication at all.)

Next, as we read math we must understand that students, not only have to attach meaning to previous knowledge, but also decode the language itself.  Barton and Heidema (2002) say:
In reading mathematics text one must decode and comprehend not only words, but also signs and symbols, which involve different skills.  
See the problem occurs that the symbols in math truly represents the unique alphabet of the language.  Not only does a child have to learn "plus, addition, more" and other words synonymous with addition but also the symbol "+".  Also, some mathematical concepts have multiple symbols associated with them.  For example multiplication could look like "x,X,*,  " or even simply a set of brackets.

For students to truly comprehend math, and find value in this language, we need to show how these symbols translate to English words.  This is where more confusion might occur as math word problems truly combine literacy with numeracy.  I am not suggesting this practice stops, but just pointing out the fact that students (especially ESL) could face another issue of dealing with a mathematical word problem.

The simple fact is how you read a math problem (or really any sort of reasoning, rational, logical, etc problem) is much different than how you would read a fiction text or novel.  The amount of information found in one sentence of a math problem is drastically higher than the amount of information found in a sentence in a novel.  Lastly, most math textbooks (and I would argue most school textbooks) are written above the grade level they are intended to be used in.

So a child/student is struggling with a word problem now what?

I remember back when I started teaching I would give hints such as "total means you should add" or "difference means you should subtract", however this is more procedural work for the child.  Memorize and output the math.  What is more important is for the child to actually hear the thought process out loud.  The first time a child encounters a math word problem, the adult (or teacher) could verbalize the actual thought process which is occurring as he/she reads the problem and truly illustrates how to translate the language of English to the language of Math.  In gradual release of responsibility model, this is called "I DO".

What we do not want from our students is simply knowing what "tricks" to employ when they see certain key words.   After hearing a child read a problem, a question which could be asked is "Are you unfamiliar with any of the words in the problem?"  Keeping in mind the meaning of a word, when it is used in math class, could imply something drastically different than when it is used in a different context.

When encountering an unknown word, simply giving the definition or asking the child to "look it up" usually is not sufficient in securing the understanding needed.

One great strategy is to use a Frayer Model, where the child would write a definition (in their own words), and provide examples and non examples of the words.

Next, ask the child if he/she is clear on what the problem is asking and to possibly read the problem out loud.  The idea of reading aloud, slows the child down and forces to not only see the words but also to hear them.  The worst thing you could do is simply tell your child what to do.  The best teachers have bite marks on their tongue to stop them from speaking.

Lastly, students need to know that certain ideas may have implied constraints.  For example a common question could be "How many ways can you arrange 3 books on a shelf?" with the common correct answer being 6.   If we named the books A,B and C then the arrangements would be


However, in reality these 3 books could be arranged in many more different ways; stacked horizontally, vertically, slanted to the left, to the right, forming shapes such as A, etc...

It may sound like difficult work, and it can be, but this work is valuable in advancing the knowledge of a child in mathematics.  The child must grow and learn to read math in a way they can internalize and ultimately distinguish information.  Simply telling a child the process is not only ineffective but can actually be detrimental to the development of his/her understanding of the concept being presented.

Wednesday, January 27, 2016

Lessons learned as I prepare for my new role

As I have now started my new role as our districts "Math and Science Lead Teacher" I look at my blog truly as my journal.  When I read my posts from time ago, I have to say that I have changed my "tune", my out look on education, and my technique of sharing.  Over the last 9 years, I have learned many valuable lessons which include:

1) You can never mandate anyone to grow, get better or learn, your only hope is to motivate someone.  This is not only true for the students who are in your desks, but also for your colleagues.  If you have a new way of thinking, and truly believe that this is superior, simply yelling louder than others, or talking about it over and over again will not only annoy others but ultimately turn them off from ever listening to you again.  Also, any idea you have heard or created may not yet be fully formed to be introduced or implemented.  Which brings me to...

2) You may be wrong!  Sure you went to a PD session which illustrates the newest, coolest, bestest (yes I used that word), thing in education, but stop and think and ask; Are you ready to answer all the questions that may arise?  Do you understand everything that was presented? Does this really mean other ways are wrong?  Are you the expert?  Most likely the answers to all of these are NO, and so be ready to stop, think, breathe and reflect on the PD.  This, of course, should not discourage you to try it and see how it fits, but don't go running to others and start telling them to change now.  Which brings me to...

3) Most times (if not all) there is not only 1 way of doing things.  Alike in math, the solution is much more important than the answer.  Furthermore, the journey has more valuable lessons than the destination (Man I love 1 liners!)  Ask any educator what do they want and I am sure the response will be similar to "All of my students to succeed", and so we all agree on the answer.  However what may work in classroom A with Teacher B, may not work in classroom C with Teacher D.  There is nothing wrong with that, nor should this change!  Which brings me to...

4) You can have high standards, and high collaboration without standardization.  Many confuse collaboration with 3 teachers working together on a task and simply splitting the work.   This is not collaboration; this is assembly line workers.  To collaborate means all working on the same task on all parts and offering suggestions.  We must also realize we can't democratize what is best for one's classroom.  Meaning, simply because the majority feel one strategy is best doesn't make it so.    Also, teachers should be able to attain the autonomy and professional judgement throughout the entire collaboration process.  Which brings me too...

5) Some autonomy may be taken away as it truly is bad teaching.  An example I think of is "Right minus wrong".  This practice to deduct marks based on wrong responses (which truly is taking off 2 marks) is an archaic practice and should not be defended by "teacher autonomy".  However, yes this goes against the first lesson I learned.  Therefore, as educators, we need to understand "why" something needs to be removed, and then offered an alternative solution.  This, I would hope, should be something that rarely occurs in one's classroom. Which brings me too...

6) Alberta has some KICK ASS teachers!! In my most current school, in schools I have had chances to work with, and in fact teachers outside of Alberta I have met some seriously amazing educators.  Students are extremely lucky to be in the presence of these people as I have met the most passionate chemists, physicists, writers, historians, religious believers, and artists in the last 8 years.  My only hope is that I continue this journey over the next 20 years.  However, if I feel like I need to change then then I shall look at my lesson 1.

Tuesday, January 12, 2016

League of Legends game club

Due to the perseverance of two students, our school recently has started a League of Legends game club.  The plan is to have students create teams up to 5 and play after school on various days.  When I held the first meeting, over 120 students, out of 1600, came to sign up.

This caused a problem as I struggled on how to organize such a large group of students!!

However, I then realized a game club had something unique that most other school teams/clubs struggle with:
  • I don't have cut anyone, as I am not governed by number of uniforms, playing time, and the constraints of the physical world.
  • All skill levels are welcome; beginners can play against beginners, and experts against experts.
  • Students literally can play from anywhere in the world, and ultimately play against any other high school in the world.
As I chaired the first meeting, which started after the cheering and high-fives stopped, I heard one student say "Finally a place where us misfits can go!".  Immediately it hit me!  Most schools foster academics with honour rolls and awards, they encourage athletics with sports teams and ribbons, and they strengthen the fine arts with band and theatre productions, but what about the "techies"?

Now,  I understand that most (hopefully ALL) schools try to allow each student some connection to their community, but at this time I had realized that at least one student had yet to have a connection with ours.  The discussions that began after my introduction were mind blowing.  Students asking "Can we have T-shirts?", "Can we make an official tournament?", "Can we play in the gathering area on the big screen for all to watch?" and of course "Can I play during class time?" (which was a quick No!)

Some students in the crowd showed such excitement and enthusiasm it was near impossible to calm them down.  We may have just hooked more students into knowing that "School is actually pretty cool!"

How did this begin?

Two years ago, I was introduced to the game League of Legends by a student.  As a gamer myself I immediately got hooked!  It is free to play, spending money won't make you have an edge, and utilizes team play.  During the summer, as I was playing, a student asked me if we could start a club.  I thought it would be an amazing idea!

During a weekend, two students and myself came to the school and developed a Prezi around "The benefits of gaming".   The prezi was then presented to our Superintendent, and Associate Superintendent of learning, and we were approved a day as a "trial".  I selected the lucky (and trust me they felt extremely lucky) 20 students to play the game while the Superintendent spectated.

The trial was a success!!

The game club has been approved, and now we are organizing our school's first League of Legends tournament with prizes to be school wear branded with logos of the game, and other technology.

I am glad that my student pushed me to start this club as I have already seen the positive impacts it can have on the culture of a school.  For information on the amazing benefits of "gaming"  I encourage  you to read the following: