Alberta Superintendents support Inspiring Education and Curriculum Redesign

This was written by Dr. Larry Jacobs who is the President of the College of Alberta School Superintendents (CASS). This first appeared as a press release from CASS in support of Alberta's Inspiring Education and curriculum redesign.

by Dr. Larry Jacobs

My name is Larry Jacobs and I am proud to serve as the President of the College of Alberta Superintendents (CASS) for 2013/14. CASS represents the system education leaders (Superintendents, Directors) for public, separate, Francophone and charter school jurisdictions in Alberta.

I appreciate the opportunity to comment on a topic in education that is being discussed in our province; curriculum redesign and specifically the Alberta math curriculum. We are fortunate in Alberta to have an education system which ranks among the top in the world. It is common for officials from around the world to visit Alberta to learn about our K-12 system. With that in mind, CASS understands that to rest on our laurels of what we have achieved in the past will not serve our students of today and the future.

One specific example that demonstrates the need to consider change has to do with the Alberta math curriculum which is generating much conversation in recent weeks. It is important to understand that many of the jurisdictions which scored above Alberta in the 2012 international math assessments implemented changes to their math curriculum ten or more years ago; the same changes that Alberta more recently has implemented within the current curriculum. 

It is also important to understand that the changes taking place in education in Alberta are a direct result of the unprecedented public input during the Inspiring Education in-person and on-line consultations with parents, students, educators and community members in 2008 and 2009. Of tremendous significance is that 63% of participants in the consultations indicated that Alberta’s education system required informed transformation while an additional 28% felt that the education system in our province required a complete overhaul. Less than one per-cent of the participants felt Alberta’s education system required no change moving forward. 

While we must consider change in order to maintain our status as one of the top education systems in the world, I want to acknowledge that the successes we have realized in education in our province are the result of the commitment by generations of students striving to excel and who are supported by their parents, their dedicated teachers and principals, and by every other person in the school jurisdictions and community that contributes to the growth and development of each child. In January of this year CASS hosted a delegation of educators from across the United States and they continuously commented on the collaborative nature of all partners in education in Alberta. 

I doubt many would disagree that many aspects of our world, including how people learn, have changed and will continue to change dramatically in the years ahead. To address these changes it is essential that Albert’s curriculum, often cited as a cornerstone of our strong education system, must undergo continuous review and revision in order to serve students of today and tomorrow. CASS supports the curriculum redesign process being undertaken by Alberta Education. Curriculum development has always been a collaboration involving Alberta Education, school jurisdictions and Alberta’s outstanding teachers and has been based on informed, researched practice. 

Curriculum redesign will enable school jurisdictions and teachers to be involved at the outset of what will be a more timely review and development cycle to ensure future curriculum is engaging, relevant and inspiring for students, who should be and must be the centre of what happens in our schools. Most importantly, curriculum redesign will ensure equity of opportunity for every single child in Alberta, a key pillar of the Inspiring Education framework that is guiding change in education in our province. 

One component of Alberta’s curriculum, math, has been the subject of much commentary recently following the release of the results of the 2012 Programme for International Student Assessment (PISA). PISA is a world-wide assessment of 15 year old students conducted every three years. While the 2012 PISA math results do show that there has been a slight decline in achievement by Alberta students (approximately 2.5% over twelve years), I offer the following for consideration: 

a. Alberta has a higher percentage of students complete the PISA assessment than most if not all jurisdictions; 

b. Alberta ensures that students of all academic levels complete the PISA assessment; more so than many other jurisdictions; 

c. the 2012 results show Alberta students performed well above average in math as compared to other jurisdictions; 

d. PISA categorizes six level of math skills, and 96% of Alberta students reached or surpassed the first level which measures basic math skills; 

e. only 4.5% of Alberta’s students achieved level six of the PISA category, which measures advanced mathematical thinking; 

f. the current Alberta math curriculum does not ‘abandon’ the basic skills of math but does also address how students can better apply basic concepts to complex situations; 

g. as mentioned previously, many of the jurisdictions which scored above Alberta in the 2012 PISA math assessment implemented changes to their math curriculum ten or more years ago; the same changes that Alberta has implemented within the current curriculum; 

h. the students who wrote the 2012 PISA assessment studied math under the previous curriculum; 

i. some of the jurisdictions whose students scored above Alberta in math see students receive tutoring in math for two hours per week and also see students doing math homework for 14 hours per week. We must ask ourselves, do we want this for our children? 

To conclude, I repeat that CASS is supportive of the curriculum redesign that is taking place in Alberta. To borrow the words of Ken Chapman who recently spoke at a CASS event, all education partners in Alberta are working together so that parents can be assured their children, who are our students, can not only be the best IN the world, but be prepared to be the best FOR the world. 

David Staples, the Wildrose and their war on teachers and learning

Here is Bruce McAllister and David Staples
 talking with Alberta teachers.

David Staples is a columnist who has an interest in education.

Bruce McAllister is a Wildrose MLA and education critic in the Alberta Legislature.

Together, they are waging war on teachers and learning by demanding that teachers teach in a way that mandates children play a passive role in school. Together, they argue there simply is not enough memorization and tests in school.

Standardized Testing

When the Wildrose and David Staples cite a real world need for annual standardized testing, I ask some questions:

1. As a columnist, can you share the standardized multiple choice test that the Edmonton Journal makes you do to keep you accountable and transparent? As a politician, would you be willing to take Alberta's Diplomas exams and have your results published for all to see?

2. As a columnist, can you share the standardized rubric that the Edmonton Journal uses to score and judge your columns? As a politician can you share the scoring guide that citizens use to score and judge your work?

4. As a columnist or a politician, can you show me the column you wrote or the bill you voted on where you are not allowed access to the Internet, fact-check or talk to anyone? 

5. As a columnist or a politician, if there were no standardized test scores, what would you know about education?

We need to stop thinking we can meet all
children's needs by pretending all children
have the same needs.

It is hypocritical for adults to demand students and teachers be held accountable in ways that they would not hold themselves to.

Standardized testing is what constitutes an amazingly contrived and unrealistic form of assessment that is used by people outside the classroom to judge and control what happens inside the classroom without ever visiting the schools.

Teachers are not afraid of accountability -- but they do oppose being held accountable for things out of their control. Teachers also know that there is nothing transparent about having children fill in bubble-tests.

The best feedback parents can receive about their children's learning is to see their children learning. The best teachers don't need tests because they make learning visible via projects and performances collected in portfolios.

This is a shift from test and punish accountability to more authentic public assurance. The Alberta Teachers' Association also outlines a vision for A Great School for All, and the Alberta Assessment Consortium offers A New Look at Public Assurance.

And here's my story about how I teach and my students learn without grades.

"Old" and "New" Math

Staples continued his war on learning with a column that featured Ken Porteous who is a retired chemical engineering professor from the University of Alberta. Porteous writes: 

The discovery approach has no place in arithmetic at the junior elementary level. There is nothing to discover.

If there was ever a need for a single statement that one could show people such that their response would predict whether they knew anything about how children learn -- this is it. 

To carry this mindset out to its (il)logical conclusion, I guess there is nothing left to discover in this world...

Teachers and other early childhood development experts who understand how children learn define their careers by children's Aha! moments. These are the moments when metaphorical lightbulbs illuminate on top of children's heads. Anyone with a clue about how children learn knows that these Aha! moments rarely, if ever, happen because kids were simply told to have them. Aha! moments are not passively absorbed or memorized -- they are actively constructed by the student with the artful guidance of a teacher.

The best teachers have teeth marks on their tongues because they know that when kids are simply told the most efficient way of getting the answer, they get in the habit of looking to adults instead of thinking things through for themselves. They understand that learning happens when the child is ready to learn, not necessarily when someone is ready to teach -- teachers call these teachable moments.

I am a huge supporter of teacher professional development where teachers learn how to be better teachers, but let's not delude ourselves into thinking that a back to basics approach that romanticizes the past will make things better for our children.

Let's not pretend that traditional math instruction didn't confuse and turn a lot of students off of math. When adults think back on their schooling, it's easy to succumb to something called Nostesia which is a hallucinogenic mixture of 50% nostalgia and 50% amnesia which distorts rational thinking.

Wishing tomorrow to be just like yesterday won't make today a better place. We aren't going to get more children to love math by pretending that school already doesn't have enough lectures, direct instruction, worksheets, textbooks, tests and memorization.

Staples and the Wildrose would like Albertans to believe that they are waging war against the government and education consultants but the truth is they are also attacking teachers who work hard to engage students in a way that has them play a more active role in constructing their own understanding with the artful guidance of their teacher.

While some teachers and parents may agree with Staples and the Wildrose, it's important to note that many teachers in Alberta feel that they are doing more harm than good. When Staples and the Wildrose mislead the public by telling teachers how they have to teach, they make it harder for great teachers to do their job.

Here's my take on the math wars, and Alfie Kohn's article answers the question: What works better than traditional math instruction?

Columnists are not Journalists and (most) Politicians are not teachers

Staples is a columnist -- which is not the same as a journalist, and I fear that too many people don't understand the difference.

He is not required to check his biases or opinions at the door -- in fact, as a columnist,  he has a better chance of selling newspapers and collecting page-views online with his biases and opinions fully intact. Staples is biased because that is his job.

Research isn't sexy and it doesn't sell unless it's accompanied by sensationalism, and when it comes to sensationalism, Staples sells the Wildrose. Making claims that teachers are no longer teaching children basic arithmetic may make for a snappy headline and a wedge issue to gain cheap political points for the next election but it couldn't be further from the truth.

As a side note, when I tried to share my math post with Bruce McAllister on his Facebook page, he deleted it and blocked me. You'd think that the opposition party would have a keen sense of appreciation for opposition, but I guess not.

"I wish a columnist and politician with no teaching experience would just
 come in and tell me how to teach," said no teacher ever.

And yet Staples isn't always wrong -- he knows just enough about education to get in trouble. His columns are filled with half-truths that are supported by cherry picked research, revisionist history and preconceived notions. He props up math PhDs, engineers, testing consultants, bureaucrats and others who have expertise in areas other than teaching young children math.

Canadians love their Olympians, but nobody confuses a hockey players' expertise for a rhythmic gymnastics coach. Similarly, a PhD in mathematics or engineering is not a PhD in early childhood development, psychology or math education.

Mathematicians are not (necessarily) Math Teachers

The best math teachers understand math and how children learn math -- these are two different skills. It is irresponsible to simply assume that someone who is good at math knows anything about how to teach it.
Just because you know how to skate or shoot a puck doesn't mean you have a clue how to properly teach young children how to skate or shoot. If you want to coach organized hockey in Canada, you are required to be educated through a certification process. One expectation is for coaches to learn the content of hockey, and another expectation is to learn how to teach children to skate and shoot.

The teaching part is so important that even if you played hockey at a high level, you would still be required to take the certification program. Knowing how to play hockey or how to do math is necessary but not sufficient for coaching or teaching -- this is why we have coaching and teaching certification programs.

Getting advice on how to teach or play hockey from someone who has never taught or played hockey is kind of like getting advice from a virgin on how to get laid. Opinion needs to be based on experience and expertise -- Staples and the Wildrose have neither.

I'm not saying that there isn't a place for columnists and politicians -- what I'm saying is that columnists and politicians need to be kept in their place, because when David Staples and the Wildrose confuse having an interest in education with being experts, they mislead people.

Here are the math posts Wildrose education critic Bruce McAllister deleted from his Facebook page

When I shared my blog post on the nuances of the math wars on Wildrose Education Critic Bruce McAllister's Facebook page, he deleted it and blocked me.

I'm not the only one.

Dave Martin is a high school math teacher and he too had his math post deleted from McAllister's Facebook page. Dave has his masters in mathematics and blogs regularly about teaching math.

Why is McAllister and the Wildrose deleting and blocking math teachers comments from his Facebook page?

Of course McAllister and the Wildrose can choose to run their Facebook accounts in any way they like but it is dishonest to then say that they are listening to Albertans.

There are many more Alberta teachers who have written about math education, and you can check out some of those posts here. 

I can't share them with Bruce McAllister because he blocked me, but maybe you could.

"Old" and "New" math

There's a lot of talk about "new" math and "old" math.

If I had to distill the math wars down to a simple idea, I would probably say that constructivist (new) math calls for an increase emphasis on understanding while simultaneously calling for a decrease emphasis on direct instruction of facts and algorithms.

The math wars get heated when critics come to see these changes to mean an elimination of basic skills and precise answers.

I would like to address three frequently asked questions about constructivist math:

Math hasn't changed and neither have kids, so why are we changing how we teach math?

Maybe math and children haven't changed, but our understanding for how children learn math is more sophisticated than generations ago.

Memorization is important and it is a very real product of learning, but memorization is not the primary purpose. Memorization is something that happens because children learn and understand mathematics first.

In math there is one right answer. Doesn't this new math just confuse kids and convince them to hate it?

Let's not pretend that traditional math instruction didn't confuse and turn a lot of students off of math. When adults think back on their schooling, it's easy to succumb to something called Nostesia which is a hallucinogenic mixture of 50% nostalgia and 50% amnesia which distorts rational thinking.

I remember dividing fractions. I was told to flip the second fraction and then multiply. It was a trick that enabled me to get high scores on tests. To this day, I have absolutely no idea why I flip the second fraction and multiply. This felt like magic when it should have been math.

If we want to confuse and turn students off math, I can think of no better strategy than to make math a ventriloquist act where children are merely told the most efficient ways of getting the right answer. When students are simply told the most efficient way of getting the answer, they get in the habit of looking to the adult or the book instead of thinking things through.

Canada's ranking on international tests like PISA are dropping. Doesn't this mean we should go back to basics and traditional math?

Since 2009, Alberta has dropped from 9th to 10th place in world rankings. A 2 per cent drop in our raw scores on math over two years has led to hysteria. The sky is not falling. It's also important to note that the children who wrote the 2012 PISA test had "old" math for their first seven years of school and only 3 years of "new" math.

My point is not to indict "new" or "old" math. There are many variables that may be responsible for the score changes. One factor is class sizes are growing. Since 2009, Alberta has added 41,000 new students and only 106 teachers.

Too many people confuse causation and correlation in an attempt to draw convenient conclusions that they simply can't prove. No one can prove that the change in PISA scores were because of teacher instruction. For example, we know that the strongest predictor of student performance on achievement tests is socio-economic status.

By idolizing PISA rankings, we risk chasing after Asian countries who achieve high scores with very different priorities and questionable means. PISA envy can lead us to aspire to be more like top-ranking Asian education systems even though those same Asian countries are desperate to reform their schools to look more like ours.

The math wars, like all wars, are ultimately destructive. Let's keep in mind that too many of us merely endured math or flat out hated it. Either way, it's safe to say that not enough of us loved it.

And we aren't going to get more children to love math by pretending that school already doesn't have enough lectures, direct instruction, worksheets, textbooks, tests and memorization.

This is a shorter version of a longer post that I wrote on the math wars here.

Jeff Johnson nails it

The math wars have returned and Alberta is at the epi-centre.

Critics are trying to blame Alberta's Inspiring Education and curriculum redesign for Alberta's 2% reduction in our raw score on math over a period of three years.

I am often the first in line to critique Jeff Johnson's handling of Education in Alberta, but I am also prepared to give him credit when credit is due. Jeff Johnson does a masterful job of explaining the nuances of PISA and Alberta's math curriculum.

It's 6 minutes long. Check it out.



Check out this petition that is in support of Alberta's math curriculum that focuses on understanding. 

PETITION: Make Math Memorable

Here is a petition by Educators For Thoughtful Pedagogy that supports Alberta's recent shift away from mechanistic pedagogy and teaching strictly through rote memorization and repetitive worksheets.

Here's what the petition stands for:

The OECD’s most recent Programme for International Student Assessment (PISA) results have

Math should be about understanding not following
instructions and memorizing.

triggered fear among Albertans that children are being used as guinea pigs for a “fuzzy” and “unproven” experiment with “discovery” learning. This fear has been exacerbated by a dominant voice in the media and politically charged critiques. The result is that teachers and parents alike have been asked to declare allegiance to either “old” math or “new” math and to defend their respective positions publicly. Advocating for more thoughtful pedagogy while under attack can be difficult and many voices in this conversation have for the most part remained silent until now. We are a group of Alberta teachers who would like to acknowledge support for our province’s recent shift away from mechanistic pedagogy and teaching strictly through rote memorization and repetitive worksheets.

While the OECD’s reported decline of Canadian student performance is not to be disregarded, the information presented by PISA is too complex to be adequately summarized in a sentence. The OECD admits that the sample data includes some “uncertainty” with respect to results and that a “large variation in single (country) ranking positions is likely.” They are also careful to clarify that PISA provides a much deeper and more nuanced analysis than mere rankings and acknowledge that it is troubling that headline rankings tend to be where most interpretations of PISA scores end. Though Canadian performance on 2012 PISA tests dropped by small margins in mathematics, reading and science, the bulk of this decline was attributed to difficulty with problem solving and critical analysis while our basic skills performance (92%) could not be substantiated as a major issue. It is also worth noting that PISA scales providing detailed information on school governance and learning environments suggested that Canadian teachers and principals felt they had very little autonomy over curriculum and assessment compared to educators in other top-performing countries. If the recent PISA report makes a strong case for anything it is for developing increased support of and trust in teaching professionals.

The “math wars” dominating educational conversation in Alberta are distracting and unproductive. As Albertans, we understand that today’s curriculum does not preclude the memorization of times tables, just as mandating “memorization” will not ensure that every child is able to commit basic multiplication to memory. It is our understanding that effective discipline-based inquiry provides space for both practice and problem solving while an overemphasis on rote memorization often becomes a substitute rather than supplement for the cultivation of deep understanding. Ultimately, we propose that the real way forward is to continue to engage all stakeholders in thoughtful dialogue that respects and acknowledges the expertise and professionalism of those who have committed their lives to teaching children in the classroom.


To:
Alberta Education

We have read "Inspiring Action on Education" and have found that the report is a good reflection of what we, our students and parents, hope for the future of learning in Alberta. We acknowledge that a broad range of educational stakeholders including classroom teachers and respected educational researchers have been invited to play an active role in the upcoming curriculum redesign. We would like to request that Alberta Education remain committed to pushing education forward by continuing to provide opportunities for teachers to co-design thoughtful discipline-based learning opportunities for students. We would also like to request that Alberta Education stand firm against demands to return to prescriptive curriculum and mechanistic pedagogy. As teachers, we have found that the determination to control things only cultivates an environment where good judgement is asked for less and less. It is the insistence that children memorize without understanding or making thoughtful decisions that has resulted in so many stakeholders who are now struggling to understand more complex mathematical conversations. The answer is not to do away with opportunities for the continued development of understanding but to remain committed to providing opportunities for all stakeholders to engage in thoughtful and considerate conversation.

Sincerely,

(your name)

Return of the Math Wars

The math wars are heating up in Canada.

First, some background: 

The math wars are nothing new. Some could argue they are timeless. Others might say they started in the late 90s when the National Council of Teachers of Mathematics (NCTM) published Curriculum and Evaluation Standards for School Mathematics which "called for more emphasis on conceptual understanding and problem solving informed by a constructivist understanding of how children learn."

If I had to distill the math wars down to a simple idea, I would probably say that constructivist math calls for an increase emphasis on understanding while simultaneously calling for a decrease emphasis on direct instruction of facts and algorithms. The math wars get heated when critics come to see these changes to mean an elimination of basic skills and precise answers. 

Let's run through some frequently asked questions from critics of constructivist math:

Math hasn't changed and neither have kids, so why are we changing how we teach math?

The argument isn't necessarily that math or children have changed, but that our understanding for how children learn math has evolved. Decades ago, when we embraced behaviourism and psychometric tests, education moved from an art to a science that said knowledge is acquired by internalization from reinforcement. Behavioural mathematics is about drill and reinforcement and might be summarized as all about teaching mathematics at students.

In his book The Glass Wall: Why Mathematics Can Seem Difficult, Frank Smith writes:

The constructivist stance is that mathematical understanding is not something that can be explained to children, nor is it a property of objects or other aspects of the physical world. Instead, children must "reinvent" mathematics, in situations analogous to those in which relevant aspects of mathematics were invented or discovered in the first place. They must construct mathematics for themselves, using the same mental tools and attitudes they employ to construct understanding of the language they hear around them. 

Maybe math and children haven't changed, but our understanding for how children learn math is more sophisticated than generations ago. Jean Piaget was an epistemologist who studied the nature and origins of knowledge, and his 60 years of research tells us that children learn mathematics by constructing them from the inside, with the artful (and scientific) guidance of a teacher and their peers. Constructivist math is less about teaching math at students and more about math learned by students.

Behaviourism and Piaget's Constructivism are both scientific theories that
have been verified all over the world. An interesting phenomenon in a scientific
revolution is that while the new theory makes the old one obsolete,
the old theory remains true within a limited scope. While Piaget's theory can explain
 everything behaviourism can explain, behaviourism cannot explain children's
acquisition of knowledge in a broader, deeper sense. Piaget's constructivism
goes beyond the primitive theory of behaviourism by encompassing it.

Memorization is important and it is a very real product of learning -- but memorization is not the primary purpose. Memorization is something that happens because children learn and understand mathematics first. Winning is an important part of sports, but we don't teach kids how to win -- we teach them how to play. Like winning, memorization has its place, but we need to keep them in their place. Like winning, memorization becomes ubiquitous because it is a feature of learning and understanding.

For more on what works better than traditional math instruction, check out Alfie Kohn's article on math.

In math there is one right answer. Doesn't this fuzzy math just confuse kids and convince them to hate it?

First of all, let's not pretend that traditional math instruction didn't confuse and turn a lot of students off of math. (Full disclosure: I grew up with traditional math instruction that included memorizing my times-tables and Mad Minutes! and I learned that I was terrible at math and hated it.) We have to be careful that our knee-jerk reaction to change isn't an act of Nostesia: a hallucinogenic mixture of 50% nostalgia and 50% amnesia that distorts rational thinking.

When my friend Dave Martin tells people that he is a high school math teacher with his Masters in Mathematics, people look at him like he's left-over mashed potatoes -- most people can't imagine why Dave would put himself through such needless torture. We have generations of adults who have graduated from traditional math instruction who break into a cold sweat when confronted with long division. For too many students, the extent of their enthusiasm for math climaxes when they are told they only have to do the odd questions. (Listen to Dave Martin debate math on CBC here.)

As for right answers, there is only one right answer if we limit ourselves to asking questions that have only one right answer, such as 4 + 3. Some of the most provocative questions that hook students' curiosity are questions that have no one right answer, such as how much does it cost to redesign your bedroom.

One of my favourite elementary math questions comes from Constance Kamii's book Young Children

Constance Kamii's three books on
Young Children Reinvent
Arithmetic are must-reads.

Reinvent Arithmetic:

Grandpa said he grew up in a house where there were 12 feet and one tail. Who could have lived with grandpa?

I like this kind of question because there are of course right answers, but there isn't one right answer. I also like it because it allows the children to construct mathematics out of the necessity of their reality. Constructivist teachers create questions, projects and games that give children the opportunity to invent arithmetic out of their reality.

It might defy common sense, but teaching children algorithms and tricks before they've had a chance to construct them for themselves actually sabotages and confuses children. Kamii writes:

It took centuries for mathematicians to invent, or construct, “carrying” and “borrowing.” When we teach these algorithms to children without letting them go through a left-to-right process, we are requiring them to skip a step in their development.

For generations, math students have asked out of frustration, "when will I ever use this?" To be clear, I'm not suggesting that everything in mathematics should be reduced to real-life application -- the significance of mathematics should not merely rest on its practical value; and yet, I would like to hear students say they use math to solve problems and understand the world rather than just to complete the odd questions from the textbook or worksheet.

I still remember being taught how to divide fractions in junior high. I was told to flip the second fraction and then multiply. It was a trick that enabled me to get high scores on the tests.

Here's the problem...

To this day, I have absolutely no idea why I flip the second fraction and multiply. I have no idea what the mathematical reasoning is. I can get the right answer on the test, but there is nothing mathematical about my (lack of) understanding for dividing fractions. If we want to confuse and turn students off of math, I can think of no better strategy than to make math a ventriloquist act where children are merely told the most efficient ways of getting the right answer. This is mindless math mimicry.

Graphics like this from Alberta's
 Wildrose Party is an effort to turn
 pedagogy into cheap political points.

The temptation to teach children carrying and borrowing as soon as possible comes from the need for efficiency, but this reminds me of what Martin Luther King Jr. said:

The function of education, therefore, is to teach one to think intensively and to think critically. But education which stops with efficiency may prove the greatest menace to society. The most dangerous criminal may be the man gifted with reason, but with no morals.

If a teacher is provided the appropriate professional development and they understand the theory behind Jean Piaget's constructivism, then this "new" math actually reflects the very essence of how people learned arithmetic before we had all these tricks and algorithms - essentially making this "new" math a very "old" math.

Canada's rankings on international tests like PISA are dropping. Doesn't this mean we should go back to basics and traditional math teaching.

PISA's rankings on their own are useless. If we focus too hard at the competitive rankings, and reduce the point of school to "test scores are low, make them go up", we risk ignoring the real lessons of PISA.

Corporate Reformers in the United
States use infographics like this to
encourage people to focus on
meaningless competitive rankings
while ignoring the real lessons
of PISA.

The real lessons from PISA are found from researching how each nation achieved their results and then assessing their methods via ethical criteria that is independent of their results. Things go very wrong when we allow education policy to be driven by circular logic: define effective nations as those who raise test scores, then use test score gains to determine effective nations. (Things go equally wrong when standardized tests move from a means to measuring education to the purpose of education.)

Since 2009, Alberta has dropped from 9th to 10th place in world rankings. Jonathan Teghtmeyer writes: 

A 2 per cent reduction in our raw score on math over a period of three years led to ministerial handwringing, parents initiating petitions, newspaper columnists launching crusades and CEOs descending from on high to chastise teachers.

It's important to also note that the children who wrote the 2012 PISA test had the old traditional math curriculum for their first 7 years of school and only 3 years with new curriculum. To be clear, this doesn't prove that "old" or "new" math is responsible for the change in PISA scores -- there are too many other variables, including other in-school factors, out of school factors and unexplained variations. When I take my umbrella to work it rains, but that doesn't mean my umbrella caused the rain. Too many people confuse causation and correlation in an attempt to draw convenient conclusions that they simply can't prove. No one can prove that the change in PISA scores were because of teacher instruction.

PISA's 2012 rankings show Finland has been replaced at the top with a handful of Asian countries (and cities). By idolizing the rankings, people might drop Finland like a hot-potato to chase after Asian countries who achieve their high scores with very different priorities and questionable means.

PISA envy can lead us to aspire to be more like top-ranking East Asian education systems even though East Asian education systems are desperate to reform their schools to look more like ours. Yong Zhao writes:

While the East Asian systems may enjoy being at the top of international tests, they are not happy at all with the outcomes of their education. They have recognized the damages of their education for a long time and have taken actions to reform their systems. Recently, the Chinese government again issued orders to lesson student academic burden by reducing standardized tests and written homework in primary schools. The Singaporeans have been reforming its curriculum and examination systems. The Koreans are working on implementing a “free semester” for the secondary students. Eastern Asian parents are willing and working hard to spend their life’s savings finding spots outside these “best” education systems. Thus international schools, schools that follow the less successful Western education model, have been in high demand and continue to grow in East Asia. Tens of thousands of Chinese and Korean parents send their children to study in Australia, the U.K., Canada, and the U.S. It is no exaggeration to say that that the majority of the parents in China would send their children to an American school instead of keeping them in the “best performing” Chinese system, if they had the choice.

If we change how we teach math, doesn't this mean our children will get a fundamentally different education than we got?

Yes.

If we want school to improve, then we have to allow it to change.

The nature of society's first reaction to changes
to school is resistance. It takes time for us to give
up our vested interest in our old ways of thinking.

People who argue that school doesn't need to improve (or should just go back to basics) are no different than a commissioner of the patent and trademark office resigning because everything that can be invented has been invented. If we are not careful, blind self-justification can mislead us to believe that the here and now is as good as it gets. Wishing tomorrow to be just like yesterday won't make today a better place.

Don't get me wrong. Change for the sake of change is no better than tradition for the sake of tradition. But let's keep in mind that too many of us merely endured math or flat out hated it -- I think it's safe to say that not enough of us loved it.

And we aren't going to get more children to love math (or school in general) by pretending that school already doesn't have enough lectures, direct instruction, worksheets, textbooks and memorization.

Unlike the Humanities, Math just doesn't have one right answer

This was written by Jeffrey Benson who is an education consultant and school coach. He is the author of the forthcoming ASCD book Hanging In: Working with Challenging Students (January 2014). He wrote the article "100 Repetitions" in the October 2012 issue of Educational Leadership magazine. This post was originally found here.

by Jeffrey Benson

All too often, math teachers sit in silent complicity when it is said that math is exact and linear—humanities are not. Math is about answers that are right and wrong—humanities are not. If math teachers don't interrupt the status quo, who will? To challenge conventional thinking about mathematics education, consider sharing and starting a discussion with colleagues around this narrative from an alternate universe:

In my humanities class, I learn that there is only one correct way to spell a word—my teacher says that spelling is not a matter of opinion. My teacher tells me to identify the word in a sentence that is a pronoun—apparently there are words that are pronouns and ones that aren't. I am told that there are fragments and there are complete sentences, and the difference is clear. If I am talking about a novel we have read, I have to tell the facts in the exact order they happened. There are rules for how you are supposed to use commas and apostrophes. I have to capitalize some words and not others—as if that really makes a difference in being understood most of the time. Those are the rules, I am told. People seem to care that I know what capital city belongs to what country, and you can't mix those up! My teacher says that some books are too hard for us to read, and some books are too easy for us, because you are supposed to read certain books at a certain age—it's developmental.

My math class is where I really get to think. Here's some of the stuff I have done:

• I made a poster explaining when it would be best to say something was "one third" and when it would be best to say it was 33 percent. It isn't always clear when you should use decimals or fractions or percents to describe a portion of something. My teacher says knowing how to communicate a mathematical idea depends on your audience and your intentions.

• I had to look at baseball statistics about shortstops and defend my reason why one of them was the best choice to get a five-year contract. Wow, that was hard! My best friend and I had very different opinions. My teacher gave us good grades for how well we prioritized the different data. He said there was no one right answer, of course—just like real life!

• My teacher put an equation on the board and said there were a few ways to solve it. He wanted us to pick a way to solve it that would be best if our life depended on getting it right; a method if we wanted to have the most fun trying a wacky way; and a method that was the quickest, even if it might sometimes cause you to make a careless error.

• He showed us a shape we had never seen before. We had to experiment with rulers and protractors and calculators and come up with the area—and then we had to come up with a formula we could remember. I love when he says, "Try more experiments. That's what math is about."

• My small group was given a big jar of pennies. We had to come up with five different ways we could estimate the number of pennies in the jar. He is giving the same problem to the kids in a class two grades below mine and two grades above mine.

My math teacher says humanities classes could be fun too, but mostly they are taught like math classes that did only number-crunching, right-and-wrong drills. He says humanities classes could be filled with opinions, creative writing, lots of discussions, and using evidence to back up our own theories. Yeah, right.

With this scenario in mind, think of ways you might flip stereotypes about mathematics teaching and learning on their head. Ask your colleagues and students to consider how to invite mathematical thinking through inquiry and employing a variety of strategies to grapple with real-world problems that don't have clear answers.

Dave Martin on how to teach math

Take 7 minutes and listen to my friend and colleague Dave Martin talk about math:

Dave backs up this interview with tons of examples from his class room on his blog.

Should Albertans panic about math?

This was written by Dave Martin who is high school math teacher in Red Deer. He blogs here and tweets here. This post was originally found here.

by Dave Martin

Edmonton Journal's David Staples has been writing about

Grade inflation and flex time harm education, high school teacher warns

and

Alberta schools are no longer the best

and most recently,

Students ‘cheated’ by way math is taught, say educators and parents

If you read all these articles, you will notice one important commonality...Staples refuses to write about the "other side" of the story. Thus I offer a view from another David.

I invite you to read his articles to see one side, and then read below to see the other.

First, Staples wrote:

It’s common for students to get much higher marks in their classroom than they get on their diploma exams...the number of EPSB students who have been graded as “excellent” or “acceptable” on province wide diploma exams has dropped by 1.9 per cent. In the classroom, however, the number who have been graded “excellent” or “acceptable” has gone up by seven per cent.

He creates an idea that this should not be the norm and the teacher mark should be the same on the diploma. This is great in theory, but before you nod your head I ask you to remember some minor details:

• The teacher spends almost 5 months with your child, while the diploma spends 3 hours. 
• The teacher has met, talked, and learned about the interests of your child, while the diploma was made in an office by people who have, most likely, never met your child. 
• Your child is allowed to use real word devices, such as Dictionaries, Apps, Blogs, Web Articles, etc, in the classroom, while the diploma creates a false sense that knowledge is only valuable if you can memorize it, not apply it.
• Lastly, because Staples writes about the Math diploma, the teacher gives various types of questions, in various formats, in various ways to your child, while the diploma only asks Multiple Choice and Numerical Response.

Now I ask, which mark should have more merit? I pose a different problem... Why is the diploma mark lower than the mark given by the teacher? Isn't it time we change our standardized assessment strategies?

Next, Staples writes:

Alberta students used to be ranked at the top of the world academically, but they are sliding...In 2000, Alberta ranked top worldwide in reading, third overall in science and math. Our teachers and curriculum were top notch and our accountability, through provincial exams, was state-of-the-art....Since then, however, Alberta has steadily dropped. This week when the 2012 PISA results came out, we ranked 11th in math, fifth in reading and fourth in science... 

First, I don't believe we can put our faith in a two-hour exam, as my arguments from above still stand, however lets go beyond that.

Staples will have you believe that this drop is due to the fact that the math curriculum has changed, and even that we need better teachers in the classrooms to be educating your child. When I read this, I remember back to my Science class when we learned about constant, dependent, and independent variables.

Before we go witch hunting on the teachers, lets remember that these teachers are the same ones who were instructing in 2000. Unless I am unaware, the graduation requirements to become a teacher in 2000 are the same as they are now. Thus, teachers would be the constant variable in this. Now that we can't blame teachers, we can ask what changed?

Sure the math curriculum changed, but was there more? Class sizes over the last year have also increased, funding of AISI projects have been reduced to 0. I don't understand how if more than one thing has changed (independent variables), how can we point our finger to one of them and ignore the rest?

My last debate comes from the fact that Staples will have you believe that because we don't teach memorization of math facts students won't understand math.

The reality is that being told number facts, and forced to regurgitate these facts, will not create an environment which is conducive to deeper learning. The best way a student can understand, not just recite, mathematics is through discovering the facts on their own. For some, this discovery process can take seconds, while for others it may take an entire class. The role the teacher plays in this is by acting as a tour guide. By keeping the students on the “path” towards the discovery, it will ensure that all students create their own individual, and innovative, techniques in learning mathematics.

I often ask myself, which skills do I want for my own children? Do I want them to be taught the skills to memorize, and ultimately be able to complete algorithmic tasks, or the ability to create and design which will lead them down a road towards a career with heuristic tasks?

The reality is that the age old saying that “Practice makes perfect”, does not apply to deep learning in mathematics. Traditionally, students have been given worksheets which have multiplication facts on them and are given a strict time limit to complete these (named Mad Minutes), but in actuality the mark given on these “Mad” sheets really does not indicate to anyone as to knowledge of the student writing them.

The weak students truly suffer the most from this model of proficiency-driven, because they find these tasks dull, repetitive, and entirely unusable in the world outside the walls of the classroom. I would agree that sometimes, knowing facts as the days of the week are important, but these facts should be a by-product of use and application not out of necessity.

Another fact is, by spending time forcing these facts to be memorized is truly interfering with a child’s innovative and creative ability. Most of these worksheets require low level thinking and usually can lock the thought process of a student into understanding simple algorithms. Eleanor Duckworth summed it up the best,

“Knowing the right answer requires no decisions, carries no risk, and makes no demands. It is automatic. It is thoughtless.” 

Is this the environment in which math students should be learning?

The new math curriculum believes, among many things, that:

• Students learn by attaching meaning to what they do, and they need to construct their own meaning of mathematics.

• Students need to explore problem-solving situations in order to develop personal strategies and become mathematically literate. They must realize that it is acceptable to solve problems in a variety of ways and that a variety of solutions may be acceptable.

• Curiosity about mathematics is fostered when children are engaged in, and talking about, such activities as comparing quantities, searching for patterns, sorting objects, ordering objects, creating designs and building with blocks

I end with a link to a petition asking the Edmonton Journal to stop writing one sided, bias, articles, and until they do so you agree to stop reading their paper.

STOP WRITING BIAS EDUCATIONAL REPORTS

New challenges, new thinking, new math

This was written by Jonathan Teghtmeyer who is with the Alberta Teachers` Association. Jonathan tweets here. This post first appeared on the Alberta Teachers` Association website.

by Jonathan Teghtmeyer

I’m a self-confessed math geek and proud of it!

In Grade 4, Mark and I would challenge each other to solve long division questions that stretched across the entire blackboard. In junior high and high school, when we were allowed to use calculators for math, I’d often forget or lose mine. Rather than borrow a calculator from a classmate, I got into the habit of doing arithmetic calculations by hand. When I was in high school, in the years before graphing calculators were mandatory, I begged my father to buy me one of the $100+ behemoths. When he refused, I used my hockey referee money to purchase one.

I understand, appreciate and value the importance of strong computation skills in mathematics. Yet at the same time, I’m dismayed by growing calls for a back-to-basics revolution in math instruction, simply because of Canada’s backslide in one international test.

Alberta physician and parent Dr. Nhung Tran-Davies has launched a petition calling on the minister of education to abandon immediately the “new math” curriculum and to embrace the basics “so that our children can be empowered by mastering the fundamentals of mathematics.”

Let’s be clear: no crisis exists. In 2000, Alberta’s raw score in math on PISA (Programme for International Student Assessment) was 550 and placed third in the world; in 2012, it was 518. We’re still statistically tied for 10th best in the world; a 6 per cent decline over 12 years is a reason to take notice, but it isn’t a disaster.

Countries that bettered Canada’s students on PISA tests have a culture of rigid and regimental skill-and-drill instruction in large schoolhouse factories; when students leave school for the day, many head straight to large-scale tutoring boot camps. We shouldn’t be surprised or concerned, therefore, that these countries outperform us on simplistic international standardized tests that aren’t designed to measure the outcomes that we desire for our education system.

I recognize the frustration that Dr. Tran-Davies must be experiencing as a parent when she sees children being taught new and unfamiliar mathematical operations with which to compute and reason. Many students will have difficulty with mathematics and will inevitably ask their parents for help. Parents likely find these new techniques and algorithms daunting and wonder why we don’t teach math the old-fashioned way.

It’s not that the old ways aren’t taught; it’s that they are included as one of many strategies that can be used. The emphasis today is on the idea that it’s more important that students understand what information they are gleaning from an operation and how to apply the right operation in a situation than simply arriving at the right answer.

This approach makes sense to me. In my time as an academic high school math teacher, I had students who could perform an algorithm and obtain the right answer to a clear question, but they struggled to explain what that answer was telling them. Similarly, they struggled with determining which algorithm to use or how to apply it when faced with a new problem-solving situation.

The new challenge facing many is the plethora of innovative tools students have at their disposal for answering questions (spreadsheets, the Internet and powerful calculators). Students are adept at using various tools to find the information they need and applying that knowledge.

Our public education system needs, therefore, to set its sights higher on the ladder of Bloom’s taxonomy. Number sense and numeracy are more important than number operations and computation. Don’t get me wrong—as I said earlier, I understand how fluency in mental math and strong fundamentals support good mathematical thinking, but we need to find a balance, and it seems the new curriculum provides that.

Standardized tests like PISA focus only on narrow assessments that measure what an international economic organization wants our school systems to achieve. Let’s push back and focus on what we want our own public education system to achieve. I want students who think critically, work collaboratively and solve meaningful problems. To achieve that, they need tools that allow them to think about problems in a variety of unique ways.

Mathematics scores are only part of the story

This was written by the Alberta Teachers' Association and first appeared here.

by the Alberta Teachers' Association

Achievement in mathematics for Canadian students is declining according to a report that the Organisation for Economic Cooperation and Development (OECD) released in December on the results of the 2012 Programme for International Student Assessment (PISA). PISA is a two-hour, paper-based standardized test that attempts to assess the competencies of 15-year-olds in 65 countries with respect to reading, mathematics and science. Randomly selected students take various combinations of tests, and school principals (with input from students) supply information about participants’ backgrounds, learning experiences and the broader education system and learning environment.

Governments around the world frequently use PISA results to “weigh and measure” the performance of their education systems. Ministers of education in Canada also use the data to benchmark their school systems over time.

How did Canada and Alberta do?

The 2012 report ranked Canada 13th in mathematics, 11th in science and 8th in reading, although each result placed Canada within a cluster of countries whose marks were not statistically different. The Council of Ministers of Education, Canada released a parallel report showing that Alberta is at the national average for mathematics and reading and above average for science. The report also shows that, if Alberta were ranked as a nation, it would be tied statistically for 10th place in mathematics and 4th place in science. The results demonstrate a decline for Alberta, which has traditionally placed near the top of the international scales.

Canada’s continued high ranking has not stopped the local and national media from expressing anxiety about the mathematics scores and speculating on possible reasons for the decline. Alberta’s raw score in mathematics has declined by 6 per cent over the past 12 years, but performance has deteriorated slightly over all OECD countries during the same period. Among high-performing countries, only Macao-China, Poland and Germany have improved their mathematics scores over the past four PISA cycles.

Is there good news for Canada?

Besides continuing to be one of the top-ranked countries in the OECD in all three subjects, Canada is one of a handful of countries that combine high levels of performance with equity in educational opportunities for students from all socioeconomic backgrounds. In the report, OECD observes that students from countries in which wealth in more equitably distributed tend to perform better in mathematics Inequity in educational opportunities can produce differences in student performance that amount to as much as seven years of schooling.

The report also singles Canada out for having teachers who promote the development of complex problem-solving skills (see infographic page 3). A significant majority of Canadian students stated that their teachers present problems for which there is no immediately obvious solution and that require extensive thought.

What’s happening internationally?

It is worth noting that the education systems that ranked highest on the 2012 PISA results—Shanghai, Singapore, Hong Kong, Taipei and Korea—are extremely test-centric and math focused. For that reason, they traditionally perform well on international standardized tests, especially in mathematics.

The reason that some countries improved in the 2012 PISA rankings may have to do with the test’s new-found ability to measure the impact of private tutoring on students’ performance. Some of the highest-ranking countries on the 2012 PISA are estimated to spend between $1,000 and $9,000 USD on private tutoring per student.

The Brooking’s Institute reports that, in top-ranked Shanghai, parents spend an average of $1,000 annually on English and mathematics tutors and that, during the high school years, the amount jumps to $5,000. In fifth-ranked Korea, 74 per cent of students received private after-school instruction in academies called hagwons. Parents spent an average cost of $2,600 per student per year on the academies. Private tutoring is also quite popular in Singapore and Japan. A recent article in Business Weekfeatured a discussion with a Japanese mother who sent her 11-year-old son to a Juku for four hours a night, four days a week, to prepare him for his junior high entrance exams. The cost of this tutoring was $9,200 per year.

According to a study by the Canadian Council on Learning (CCL), one-third of Canadian parents have hired a private tutor or tutoring company for their child. In most cases, the students involved were already average or high achievers.

Implications for the future

Focusing on external rankings based on standardized tests may draw attention to students whose performance is marginal and increase the demand for private tutoring. The CCL study suggests that, during the 1990s, the number of private tutoring companies in major Canadian cities grew by between 200 and 500 per cent. Digital tutoring and adaptive learning systems are playing an increasingly dominant role in the tutoring industry in North America. In 2013, Dreambox Learning Inc., a technology company based in the United States, claimed that its intelligent adaptive learning system was as effective as human tutoring in accelerating math teaching and learning. For countries attempting to achieve excellence through equity, tutoring—because it is available only to the more affluent—may actually exacerbate disparities.

Recommendations for Canada

The PISA report includes recommendations for countries like Canada in which mathematics performance is only weakly related to socioeconomic status and in which socioeconomic groups tend to perform at nearly the same level. The report recommends that such countries should strive to improve performance across the board by changing their curricula and instructional systems and by improving the quality of their teachers. This recommendation is likely behind Education Minister Jeff Johnson’s response to the 2012 PISA. The report suggests that teaching quality can be improved “by requiring more qualifications to earn a teaching licence, providing incentives for high-achieving students to enter the profession, increasing salaries to make the profession more attractive and to retain more teachers, and/or offering incentives for teachers to engage in in-service teacher-training programmes.”

Started in 2000, PISA is administered every three years. The subject of focus in each cycle rotates among reading, mathematics and science. PISA 2012, the fifth iteration of the testing program, focused on mathematics. Approximately 2,500 Alberta students from 100 schools took the tests.

Grading Moratorium: Dave Martin

Dave Martin has joined the Grading Moratorium. Want to join? Here's how.

Dave Martin

Red Deer, Alberta, Canada

High School Math

teacher.davidmartin@gmail.com

@d_martin05

I started teaching highschool Calculus at my school a couple of years ago. When I started teaching the course, I used a traditional assessment strategy. I would assign homework daily, end the week with a quiz, and then end the unit with a multiple choice/written exam.

My classes would start around 30 students, and by the end of the semester the class size would be 20. What I did was "weed out the weak". One day I realized that I wasn't weeding out the weak mathematicians, but instead weeding out the weak test writers.

This year, after many talks with first year University and College professors, administrators, teachers, students, and parents, I am proud to say that I have abolished grading. We are currently in the middle of our semester and I have not graded a single item of student work.

Before you continue, I want to remind you that this does not mean I have not assessed, but not one student in my Calculus classes has received a grade at this point. (Other than the report card mark which I must give).

How does it work?

First, I went through my outcomes, given to me by the government, and identified what the "Rocks" are. These rocks are the outcomes which I expect the students to master above all other outcomes. I chose these certain outcomes after my discussions with others and as well as what will be helpful for students to succeed in the future.

Next, these outcomes were rewritten in student friendly language and then provided to the students on the first day of class.

My teaching schedule did not change, nor did the speed on which I have taught the course, but what has changed is the speed at which the students can learn at. Once I had taught 2 or 3 outcomes at a level where I felt that the class has mastered the outcome, I administered a summative assessment. For this assessment, each child wrote it as a traditional exam, but it looked drastically different than a traditional exam. Each assessment was entirely written, broken up by outcomes, and tested only the basics of the outcomes. There were no "trick questions", just simple questions that would assess "Can the child demonstrate this outcome, on their own, as a basic level of understanding?"

When I assessed these assessments, I would write comments only on them, and either a "Outcome demonstrated" or "Need to learn" for each outcome assessed (Not on the overall assessment). It is very important to understand that "Outcome demonstrated" is not a 100%, as a student could make a minor mistake and still achieve this, as I am assessing understanding the outcome, not perfection.

Next, if the child received a "Need to learn" he/she must do the following:
1) Demonstrate the understanding of the questions given at a later date. This usually occurs after a lunch session, a quick conversation, or multiple conversations with the child.
2) A conversation explaining how he/she made the mistake earlier and how their understanding has changed now
3) Write another assessment on the outcomes.

If after completing these 3 steps, he/she can demonstrate the outcomes then I would I count this as "Outcome demonstrated" just as if the child had done it the first time. I do not deduct marks based on the number of tries needed.

If the child still does not demonstrate, (which is extremely unlikely as I have seen) then he/she must repeat the same 3 steps.

After 5-7 outcomes have been taught, then each child is assigned an open ended project. This project consists of each student creating a problem around the math in the 5-7 outcomes and solving it. The expectation is the problem is one which is deep, relevant, and for a purpose. This part is not always easy!

An example: A student to demonstrate his understanding created a Call of Duty video and determined the rate of change of a ballistic knife falling in the video.

These projects usually range from 3-5 pages and must be handed in individually, but can be worked on with assistance from others and/or textbooks.

To assess these projects, I follow the same pedagogy from above. I use comments only, and give guidance towards any errors I see. The projects are then handed back to each student, who can go back, make corrections, and rehand it in. This process is repeated until the child receives perfection on the project.

I have even abolished the traditional final exam. The expectation is the students must give me a 30-45 minute presentation around the rocks of the course, and demonstrate their understanding of all rocks.

How do I get a final mark percentage?

I simply take the number of outcomes and projects completed (at the end of the course) and divide by the total number of outcomes and projects. This is not the best strategy, but it seems to work for me at this moment. I do weigh projects twice as much. (I have 20 outcomes, and 5 projects, so the total is (20+5x2=30)

Let me know if your thoughts

Stop writing the objectives on the board

How often have you been told that writing the lesson's objectives on the board is best practice? Can you think of even one reason why doing this might be a bad idea? Because the prevailing wind of conventional wisdom consistently blows in favor of content-bloated, prefabricated externally mandated standardized standards, it takes courage to pause and reflect.

Mike Fishback offers this post titled Objectively Speaking where he identifies three reasons why we should question the wisdom behind writing the lesson's objective on the board.

1. Communicating objectives to students sends a strong message about who is driving the learning.
2. Communicating objectives to students gives away the ending before the uncovering even begins.
3. Communicating objectives to students discourages students and teachers from pursuing potentially constructive lines of inquiry that appear tangential to the objectives.

I often share this clip of Alfie Kohn telling a story of a grade one class discovering the need for standardized measurement.

Watch this clip and think about what affect writing the objective on the board would have had on student learning.



I think we can all agree that writing the objective on the board might have ruined this experience in some way for some of the kids. When I hear that teachers are mandated to write the objectives on the board and are subject to being evaluated based on their compliance, I become concerned.

At the very least, teachers should be afforded the professional responsibility to decide whether writing the objective on the board is pedagogically appropriate.

Adding to 10

Here is a game I use to help students with adding to 10.

I introduced this game to Jonothon, who I knew was a weaker student with some underdeveloped math skills.

The moment I said that I had a math game for him to play, his face turned white and I could see his anxiety level immediately skyrocket. Math for Jonothon is not something he would associate with a game.

But with some encouragement, he agreed to give it a go.

However, once he saw the game had a timed element to it, panic struck again. So I calmed him down and said that winning or losing the game meant nothing, and that I had lost this game more times than I had ever won. He took great comfort in my failure but was still hesitant.

With some further encouragement, he decided to give it a try; however, I could quickly see why he was likely so hesitant - adding to ten was not something Jonothon was very comfortable doing. So after watching him randomly shoot numbered balls all over the place, I got him to stop playing and grabbed a piece of paper. Together, we wrote down all the combinations for adding to 10:

1 + 9 = 10

2 + 8 = 10

3 + 7 = 10

We got this far when he stopped me in disgust, "No, no. I don't want to write it this way."

"Why?" I asked.

"I don't like how the numbers count down from 9 to 8 to 7. I want them to count up."

So he wrote:

9 + 1 =10

8 + 2 = 10

7 + 3 = 10

He got this far when he stopped and said, "Hey, wait a minute - these all add up to 10."

If someone could have taken a picture right then and there, you would have seen a giant lightbulb over Jonothon's head and a smile from ear-to-ear on my face.

Jonothon then went back to the adding to 10 game, where I watched him check his piece of paper (that he created) before ever shooting a ball.

But then something happened.

All of a sudden I watched him take a 2-ball and shoot it at an 8-ball without looking at his paper. Both balls disappeared. He turned to me, smiled and said, "Did you see that?"

I smiled back and said, "yes, yes I did."

I didn't need to praise him - my presence was enough. I didn't need to marinate him in "good jobs", he just wanted to know that I was watching, and I was.

It is precisely these kinds of observations - these aha moments - that teachers make while the children are still learning that are so important, because to be honest, there is no substitute for actually being there for these moments. This is the most authentic and direct kind of assessment educators do everyday.

What's really kind of weird is that more we try and quantify these kinds of aha moments, the more we squash them.

Lunch time came, and Jonothan was disappointed that he had to stop playing. Before charging his laptop to scamper off for lunch, he turned and asked, "Can I play more math games after lunch?"

To which I gave the only appropriate reply, "yes, of course."