Number Talks

How do you foster numeracy in a math class?

Very simply; Once a day, for no more than 15 minutes, complete a Number Talk.

What is a Number Talk?

Simply put, a Number Talk is a "naked number question" where students must use mental math to arrive at the answer.  This tasks removes the myth of "there is only one way", or "there are better ways than others to do math" and instead ensures that all students are aware that each of them have some sort of mathematical insight to offer everyone else in the class.


Here is an example...

In Grade 2, Jennifer Smith put this up on the board and asked "How many dots are there?". 

 After most of the students said "7", she asked "How did you count them?", and this begins the Number Talk.  I will let her share her story:

 I was surprised that they had this many different ways of counting the dots and my class had no trouble explaining their thinking. I even had a girl; say 5. I was careful and said come and show us and she pointed to the middle 5 and then said oh ya and 2 is 7.

Now the cool part!!! 2 girls even asked to stay in during lunch and continue to count the number of ways to count to 7,  (This is Grade 12 Math outcome!!)

Number Talks are a great way to get students talking, explaining, reasoning and ultimatley arriving at a deep conceptual understanding of how numbers work.  If you are interested in knowing more I would suggest you read the following book:

"Making Number Talks Matter"

Is Streaming an Intervention Technique?

Streaming, or tracking, students occurs quite regularly around the world.  This means that, at some point in their K-12 education, they are grouped by ability or intelligence.  Many educators and parents support this idea.  The philosophy, behind this practice, is that it allows for teachers to teach groups of similar intelligence levels.  Also many believe that the high end students, through streaming, can be enriched on topics beyond the course.

This streaming occurs at different ages, or grades, in different countries.  In Alberta, streaming usually occurs at grade 10, while in USA this practice starts in middle school.  Finland, an international leader in education, has outlawed streaming entirely.  This then begs the question, "What is best practice for streaming students?"

Some educators, who support streaming, say that this practice allows them to teach to "like-minded" individuals and the need for scaffolding diminishes as there is a homogeneous group in front of them.  The material, consequently, is presented in such a way for the "average" of the group to understand; using the logic that all students are more or less the same.

This, unfortunately, contradicts almost all research around the growth of individual students.  No matter how well you group students based on ability, there will always be some students who may find a certain topic easy, and other topics more difficult.  Teaching to the "middle" will actually cause some students to struggle while preventing others from being enriched.  I also fear, in an education system where streaming is prevalent, the practice might become, "If you are not understanding, you must simply be in the wrong stream".

In a mixed-ability class, the teacher is forced to create material that all levels can benefit from, where the top students are challenged while the weaker students are comforted.   This results with all students learning at the highest of their levels and a philosophy of teaching that "all can succeed".

Also, when students are streamed, certain stereotypes occur.  Early in my career, this was a regular occurrence for myself.  I remember thinking while teaching a dash-2 course (a second stream in Alberta) "Well this is the lower stream so they won't be able to handle this..." or "We won't have time to do that project, as my students will take longer to learn...".  This ideology is harmful to students.

In 1960, Rosenthal and Jacobson conducted an experiment to look at the impact of teacher expectations.  Students were randomly placed in two groups, regardless of ability or talent, and these groups were labelled as "smart" and "weak" for 2 teachers.  After a certain period, they determined that actually the "smart" class had scored at higher levels on IQ tests, while the "weak" class struggled with many concepts taught.  Expectations from teachers was the difference.

This stereotype, once placed, becomes almost unbreakable.  In England, where they stream by age 4, it has been shown that 88% of children remain in the same groupings until they leave school.  This should be alarming!! A label, we give to a person who should be playing with blocks, dolls, and laughing, will determine his/her success for life!  This, again, contradicts almost all research around child development and learning.

This label is not limiting only the weak students but also the "smart" ones as well.  Carol Dweck, found that the moment students are streamed, by ability or intelligence, the students who were most negatively affected were those going into the top rank.  Their positive growth-mind-set thinking reduced almost instantly, and they became fearful of making mistakes and consequently avoided more challenging work.  This was especially prevalent in high achieving girls.

Students and parents usually support streaming due to the fact that this practice can allow schools to prepare students more appropriately for their future.  This argument is actually flawed.  Jo Boaler, followed students from two different school experiences.  The first group came from a school where they organized students heavily by ability, while the second school mixed all abilities together.  She found that the students who experienced mixed-ability grouping, despite growing up in one of the poorest areas in the country, were now in more professional jobs than those who had experienced streaming.

What is even more interesting was the attitude of the students who learned in mixed group settings.  At first some of the brightest students were aphrenrsive around the fact that they would be constantly explaining their ideas to the rest of the class.  However after one year this changed as they were quick to realize that this practice actually helped them understand the concepts being taught.

What is the solution?

Simply don't stream students based on prior knowledge or ability.

A great practice I have seen comes from a colleague of mine, Jonathan Mauro.  He is the department head of a high school physical education group and has started a creative way of streaming; he lets the students decide.  Instead of saying, "this group has high physical literacy, and this group has low physical literacy", he provides the students options of engaging in physical literacy.  3 full classes are scheduled during the same time slot and then the 3 teachers teach each unit using a different sport or activity to address the PE curriculum.  Meaning, one student can learn through volleyball, while a different student can learn through badminton.  Regardless of previous ability or experience, each student is free to choose which activity would be most engaging to them.

More to the PISA scores

Many people try and use PISA test data to infer that there is a problem with Math education in their area.  I have seen this argument used in many blogs, papers, and social media outlets.

Initially, some people will show fancy graphs and try to convince others that the drop of PISA results has actually been caused by a change in curriculum.  Later they will conclude that unless we dig up some old curriculum these scores will continue to drop in the area of mathematics.

First, any arguments, at best, truly show that there is only a correlation between the type of math curriculum their area has and a drop in PISA data.  All arguments (which I have seen anyways) always fails to show causation.  What is the difference?

Correlation is when two or more things or events occur near or around the same time.  These things might be associated with each other, but are not necessarily connected to each other by a cause/effect relationship.

An easy example is when people get a cold during the winter months they usually end up with a runny nose and a sore throat.  These two events are correlated but we cannot conclude that a runny nose will actually cause a sore throat to occur.

Most arguments around PISA, tend to show some sort of data analysis and link it to a change in curriculum, and again this would be correlation, at best.  However, we can take a closer look at the data ourselves...






If we look at the Canadian results of PISA by province, we see that every single province dropped from 2009 to 2012, other than Quebec and Saskatchewan.  On the international level, Netherlands, Belgium, Australia, Denmark, New Zealand, France, and many other countries fell at similar rates to Canada.


If there is a Math Crisis in your zone, then there must also be a Math Crisis around the entire planet? Does this sound likely?  I would hope not!

Some "back to the basics" folk will ignore the fact that they are implying here is an International Math Crisis and simply tell us that:

 PISA tells how well the math curriculum is in a certain area compared to other parts of the world.

 Well here are some stats that show how false that statement is:

Shanghai had the highest score on the 2012 PISA test with an average of 600.24, while Australia had a much smaller average of 515.01.

What can you conclude?  That Australia's math curriculum is much weaker than Shanghai's?

If we look at students who were born in China and moved to Australia before ever entering school, their average on the 2012 PISA test was 614.77... 14 POINTS HIGHER THAN SHANGHAI!!!

This must mean that Australia's math curriculum is superior to Shanghai's?  See the problem?

Using PISA scores, alone, to determine the quality of education in a province, state, region, or country is similar to judging someone's ability to drive simply by only watching them parallel park. While this single test can make many great observations around education on a global scale, we need to realize that it is exactly that: a single test.

There are much more variables at play in an Education system than simply the results on a test that some countries value more than others.  If you attend school in Scotland and are called to write PISA, you will be forced to watch champions winning Gold Medals for their country and informed that you have the ability to "bring home the Gold for Scotland".

If you attend school in China and are called to write PISA, your name will be broadcasted and people will cheer you on as you walk into the testing room.  The test you will write will be similar to the test preparation you have received over the previous months.

If you attend school in Canada and you are called to write PISA, you will be quietly removed from a class, brought to a room to write a test you know nothing about and have had no formal preparation for.

So I ask again, does a drop in PISA scores really mean a math crisis?  I think not!

Lastly,  we need to understand that a lot of arguments against current math practices are actually attacking teachers and not curriculum.

Further Reading:

Sam Sellar- Globalizing Educational Accountabilities
PISA Key findings

Where do the misfits go?

Algebra Day 1

Some points after reading Connecting Math Ideas by Jo Boaler on creating algebra.  Also a great activity to have with students, or yourself.

Tell your students the following everyday

• Addition, subtraction, multiplication, and division is part of math but math is so much more!  While algebra is a focus in many classrooms, don't forget about geometry, probability, or data analysis.
• You can't make understanding an algorithmic process.  Students need to experience confusion, misunderstanding, and failure as part of the understanding process.
• Being good at math is not something that is easily explainable.  Accuracy and speed in procedural mathematics is only one way.  Other ways include being open minded, logical, discussing conjectures, and trying to answer "why?".  Everyone can be good at math and we need people who can do math in those different ways.
• While a problem may only have one correct answer, it may have many different correct solutions.  While some solutions are more efficient, or effective than others, it is more important that everyone understands at least one way of arriving at the correct answer.  Math must make sense.
• We can get better at certain skills of math by practice, however talking and discussing with your fellow students will allow you to understand mathematical ideas deeper.

When developing algebraic thinking with students, we shouldn't force students do what is the most efficient (as sometimes this is objective anyways), but to do what makes sense.  When presented with a set of data, or a pattern, Thorton (2001) argues that it is less important that students be able to find the algebraic rule than they recognize a rule can be represented in equivalent algebraic expressions.  When "finding the rule becomes the focus" most mathematical thinking is lost.

Lets, for example, look at the following grid.  I want you to tell me how many blocks are coloured in this 10x10 grid without counting the blocks individually.  It is crucial you do this without writing, talking to a partner or counting, as it will force your mind to make generalizations which will be the basis of deeper learning to come.  

As a teacher we should first ask students now to share answers, not strategies, with an elbow partner.  This would then force some to reevaluate their strategy and possibly pick up any common errors he/she may have made.

Now how did you do it?  Here are some strategies in Arithmetic form:

4x10-4

10+9+9+8

10+10+8+8

10x10-8x8

4x8+4

As a reader, are you able to explain how each of the expressions above arrive at the same answer? An important task in furthering one's mind into algebraic thinking.

Imagine if this was done in a classroom.  Jason stands up and explains why he simply went 4x10-4.  There might be some smiles, nods, confused looks.  Some students will have seen the same answer provided a different way.  Does this happen on a worksheet?

Of course now, you have realized that the correct answer is 36.  Would then the expression "30+6" be appropriate?  This is where conceptual differs from procedural.  Yes 30+6 equals 36 but unless a child can create meaning to the 30 and to the 6, I would disagree that 30+6 would be an appropriate response in this context.  This illustrates the idea of solution(30+6) vs answer (36). 

What if the grid was 8x8, how would the above expressions change?  Would a number change in every expression or only some?  This idea of visualizing a problem and solving it, is crucial to the advancement of one's knowledge.   

Going back to your strategy and stretching the square to an unknown length, could you create a verbal description of what would you do?

Now the algebra begins..but first...

Noss, Healy, and Hoyles (1997) point out that somewhere we stop seeing algebra as a tool but instead of the end point of a problem. The confusion starts when we see problems as a way to practice algebraic skills instead of using algebra to explore problems.

When bringing in letters into these expressions we must remember some powerful pitfalls:

• The largest misconception is that letters are labels or initials. (pg 25)
• Changing the variable to a different letter changes the solution.  (Let students pick the letter, and encourage different students with different letters)
• The equal sign simply means "gets the answer". (Try writing 5=2+3 as often as 2+3=5 especially in earlier grades)

Taking these points into account, create a variable for the side length of the square.  Could you create an expression using your variable to show the amount of squares which would be shaded?  Knowing what you have done so far, how could you test your expression?

In a class at this point it would be helpful to ask the class "What will be staying the same? What will be changing? As we bridge the gap from numbers to a variable".   For example if the strategy you are using is 10*10-8*8, then the multiplication and subtraction will remain the same while 10 and 8 will change to x and x-2 respectfully.  I would not tell them this, but instead question it.

If you followed all of these tasks then you have now done the problem in 3 different approaches: Arithmetic, Verbal, and Algebraic.

The crucial part of this example, or if this lesson was to be developed into a classroom, is to ask questions and not simply give answers.  Remind them we are not seeking the solution, but a solution that makes sense to them.  Embrace students' wrong answers since learners who are given competing ideas, engage in cognitive conflict and such conflict promotes learning more than the passive reception of ideas that are always correct and seem straightforward (Fredricks, Blumenfeld, and Paris 2004).

PBL on Math 30-2 Research Project

Here is my attempt to create a PBL for a High School Math class.   In WCNP, in Math 30-2 and 20-2 there is an actual outcome around researching a topic and relating it to math.  Below you will find all resources and timelines.  Please feel free to use, change, alter, as you see fit.

PBL Math Research Project

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!

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 there was a focus to teach it one way and all students were required to learn that one way.  Finally, alternative efficient strategies are not only accepted but encouraged!  We are allowing students to not only learn math, but actually like it!

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.

Body:

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).

Year	Population (Billion)
2016	7.4
2015	7.3
2010	6.9
2005	6.5
2000	6.1
1995	5.7
1990	5.3
1985	4.9
1980	4.4
1975	4.0
1970	3.7
1965	3.3
1960	3
1955	2.8

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.  

Conclusion:

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.   

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

ABC   ACB   BAC   BCA   CAB   CAB

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.

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.

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:

https://www.apa.org/pubs/journals/releases/amp-a0034857.pdf