EDUC115N Review #9

I am going to post one of my answers to a question in the course. This is about the process that students need to use when encountering math problems.

My metaphor: Brain Building Construction Zone

Students will be taught the metaphor that doing math is like building your brain, and every math problem is a brain building construction zone. 

When given a math problem you don't just jump in and start building the answer you have to slow down and read the signs. Students will be taught that in this construction project, when given math problems to solve there are important steps to follow: 1) Say it 2) Draw it 3) Estimate it. These are the pre-building steps that students need to slow down and pay attention to. If they don't understand enough to make an estimate than they need to stop and go back to the drawing board. This is like making an estimate for a customer. Before they build they need to be able to describe what their end product should look like, just like in the buildings and materials trades. 

Pre:Build = Before Solving
1) Say it 2) Draw it 3) Estimate it

Once their customer has agreed to their estimate then they can build. To build they need all their math tools, and they need the right tools for the job. Most of the explicit teacher directed math lessons will happen here. Sometimes they may not have the tools and may need to learn how to use new tools. 

Here is a math tool. 

When they have mathematized they need to test their building project and refine or revise as needed. Once done they step back and look at their project to see if it is ready to be sold. Can they describe it to a potential buyer in a way that makes sense. Has their project actually been built, or is it just a mess of math material that nobody understands?

Describe it and revise if needed.

To recap. In the math brain building construction zone, stop and read the signs, then say it, draw it, estimate it. Then build it with your math tools. Make sure it is perfect by refining and revising. Then sell it to the customer by describing it in a way that makes sense.

The process will help students see math as a creative act that they control. 

EDUC115N Review #8

Number Talks #2

In my last post I introduced the idea of number talks. As I worked through session five of the How to Learn Math course I was shown examples of number talks from a college classroom and a grade three classroom. Granted the students in the college classroom were being taught how to use number talks, but the task still helped them understand math on a different level. 

One of the thing I am noticing is that students need to have a firm grasp of the times tables for this level of math to work, so as I think about teaching my strategies class part of the class will have to be dedicated to helping students memorize the times tables. Number talks can help with this, but I really believe the times tables will have to be visited everyday.

One method used in the number talks lessons was the use of dot cards. Students were shown dot cards and asked to describe to their peers how they added up the number of dots. This process had students talking mathematically and with precision. The teacher then created visualizations of what they were saying. It was really quite surprising seeing how ten dots on a piece of paper helped students learn the key lessons: numbers can be broken down, they can be manipulated, they can be decomposed into "friendly numbers."

After the dot cards lesson I saw how number talks were used to develop an understanding that math is far from static or concrete. Number talks gets students talking about creative, but precise, ways to solve problems in their heads. It gets students doing the talking and the explaining instead of the teacher, and number talks concludes with a visual representation of what was solved. This is a practice that will work in a jr. high classroom. 

EDUC115N Review #7

Now we are getting into the meat of this course. The work of developing a growth mindset is a year-long pedagogical guiding point, one that needs to be taught, developed, revisited and reflected upon, but what should the day to day math lessons look like? I know some big ideas have been mentioned in the class, and here in this blog. Students need to make sense of numbers, talk with each other when trying to solve problems and be given the space to think creatively about math, but again, what about specific lessons.

Enter Number Talks. An idea and a method of teaching that can be used everyday in the math classroom, in order to increase fluency and automaticity, and, at the same time, help students with the conceptual understanding of numbers.

Not Quite what I meant

Number Talks is all about freeing a students mind from thinking that there is only one way, one right way to solve problems in math, and it works like this:

1. Give a problem with the instructions that you can't write it down or use the traditional method of solving it. ex) 18 times 5
2. Have students share and describe how they got to the correct answer. At this point students are learning a) how to talk about numbers or b) how other students think about numbers.
3. Talk about the different methods that are used. Here the teacher can step in and create visual representations of the student's explanations. Many of the rules of mathematics can be explicitly taught here.  

Having kids solve problems in different ways teaches them number sense. It teaches them the ability to break numbers apart, or decompose the numbers, and regroup them. This ability is a key foundation for all of math. It also teaches that math is creative and flexible. With activities like number talks students walk away from their math lessons understanding numbers, instead of blindly remembering and following formulas. 

EDUC115N Review #6

This is the half-way point of this course, and I want to offer a little review of the major idea of the course. I was able to tell a family member about this course yesterday, and he asked me, "so what does have to say about how to learn math?" I was happy that I actually had an answer to provide.

Stanford, through prof. Jo Boaler, is very clear about what students need in order to learn math. Students need to develop a growth mindset. They need to know and believe that they, everyone, can learn and understand math. Not as a, "you can do it!" false self-esteem thing, but as a fact about their brains, "anyone is capable, with hard-work practice and the right teaching methods, capable of succeeding at math. Students need to be taught how their brains work, given the opportunity to experience real learning, and reminded often that all students are capable of growing their understanding.

How we teach, allowing students to struggle, talk to one another, find different approaches, and make sense of the math they learning. How we help students in the classroom, praising mistakes, withholding answers, keeping things open to students thinking. How we assess, providing feedback instead of grades, celebrating mistakes as opportunities for learning, focusing on growth. All of those things, that is how students learn math.

EDUC115N Review #5

This is one of the posts I have been wanting to write because it concerns a topic I have often discussed with colleagues and people not in education. Many many teachers and even more people not professionally involved in education believe that ability based groupings of students makes sense, is best for students and is the most effective way of organizing a school in order to help teachers be successful. I have always disagreed with ability based groupings, and it turns out, so does professor Jo Boaler, professor of Mathematics Education at Stanford University.

One of the reasons people like ability grouping is because it makes sense in their normal life, and in their learning outside of school. Someone that has never done Yoga would not enter into an advanced yoga class, and why would someone that is great and experienced at Yoga go to a beginners class?

Not for beginners

The question is, should schools, particularly jr. high schools take the common sense approach called ability grouping or tracking?
The answer is no, and here is why: it encourages, in all students, a fixed mindset. Whether a student is placed in the high, medium or low group they develop fixed ideas about their ability. Even the students in the high group think they are there, not because they work hard and persevere when given challenging work, but because they are the smart kids. When students realize they are in the low group everything begins to unravel. The EDUC115N course says it nicely.

There are many pieces of research, and other valid reasons for why ability grouping just doesn't work. The Fixed mindset versus a growth mindset is one of the most compelling. 

EDUC115N Review #4

I am eager to share some thoughts that have come in this class about ability grouping, but I am going to save that for my next blog post. This one will be short and it will be about assessment.

In the How to Learn Math class that I taking one of the ideas discussed is the value of formative assessment. Now, teachers at my school are relatively progressive about assessment, so they are already quite aware of these ideas, but there are a couple of notions that deserve to be heard again and again.

but it's a valuable story

1.  Feedback is more valuable to a student's learning than a grade. "Students who only got feedback scored significantly higher than ones given a grade or a grade and feedback." The best thing you can do for your students is to ditch the grade and give them diagnostic feedback.
2. Students need the opportunity to practice self and peer assessment. What would this look like in the math classroom? Students given access to the learning goal of a given lesson and assess where they are in their understanding. Then students are given the opportunity to work with each other, problem solve together, discuss solutions and peer assess each others ability according to the lessons learning goal. 
3. After low achieving students spend time discussing and assessing themselves and others they will start behaving like high achieving students. 

This is what assessment in the math classroom needs to look like. It is tradition and the need to classify and group students that insist on having big unit exams with grades given to students. These are not necessary practices, and are in fact harmful because they create a fixed math mindset in students.

I know that this is controversial, but wait until the next blog post...

EDUC115N Reflection #3

Lots of great ideas in session four, but I think the best way to share what I am learning is to share what I am learning. Check out the link below to see the difference between how math is taught and how math ought to be taught.

When I let them own the Problem

Here are my ideas about the problem:
The initial wonder, creativity, and questioning would be so much more interesting to students than a problem in a textbook. I also appreciate how students would have to measure the lines and angles that they drew with ruler and protractor. All of the questions in a text book have nice rounded distances and angles for students to work with that they never get to apply their measurement and drafting skills to an actual problem. Bringing real life measurements into the math problem will develop skills that the students need. Students need to be open to different methods of solving a problem. There is not only one way to do it, but in order to reinforce the lesson, and in order to make sure students have achieved the learning goals, having students work on each others drawings is brilliant. As always, making students explain to each other puts even more learning on the students. I can hear the math teachers I work with objecting that the teacher who wrote this blog took a 20 minute lesson and turned it into a lesson that would take two classes, but the results are worth the time it would take. Instead of only 40% of the class understanding and only 10% of the class enjoying the lesson the teacher should have 100% of the class understanding, 40% of the class having a deep understanding and almost all of the class also enjoying the creativity, skill development, and real world application of math.

Which type of math question will create future engineers?

EDUC115N Reflection #2

Now that I can access google apps again, here is what I am taking away and will use from my Stanford online math course.

The math classroom matters. The environment that is created for the students when they enter and experience the math classroom is crucial. When I talk about the environment I really mean the mental environment. How one physically organizes and decorates the classroom can impact the mental environment, but it really comes down to how the students feel when they sit down and begin to learn math.

Students need to feel safe to make mistakes.The importance of speed needs to be eliminated. A growth mindset, as opposed to a fixed mindset, needs to be taught and encouraged. These three ideas will almost certainly run counter to a student's pre-existing ideas about the math classroom, so they will have to be explicitly taught and modelled. Mistakes will have to be celebrated, the teacher will need to prove to students that all are capable of learning math and growing as a person, and assessment practices will need to change. 

To stick with this assessment idea a moment longer. What does it mean to be successful in the math classroom. Traditionally it means getting through the curriculum and doing well on math tests. Is that really creating students that will have successful careers in Science, Technology, Engineering and Math? Of course not. Our assessment practices need to encourage a growth mindset by providing positive individual feedback. We need to stop moving through the curriculum before all students have experienced success with the content. 

Just to reiterate, the ideas above are coming from Stanford math professors. More to come...

How to Learn Math: EDUCN115 from Stanford University

I will use this space over the summer to share and reflect on my experience taking a free online course from Stanford University titled: How to Learn Math.

The fact that there I can take, for free, a course from an Ivy league school is exciting and potentially powerful. We will see.

The first thing about this class that I am excited about is that there will be a course for students offered in the Fall. I hope I can register our strategies students, if this turns out to be a good course for them.

Positive experience with the course #1: Click pause, change a diaper, back to math class.

Key take aways from the introductory session:

1. Make sure your students know that you have high standards, and that you believe in their ability to achieve them.
2. Math stereotypes can be debilitating and need to be actively combated. 
3. Students should use their imagination in the math classroom. Indeed, it could be the only subject that can operated unencumbered by reality. Why imagining a perfect circle should be an artistic endeavour. 

The Cell Phone Debate has Been Ignited

After having just read a post from Scott McLeod's Dangerously Irrelevant Blog on The Unholy Trinity of Classroom Technology Uses I wanted to get out a couple of thoughts on the upcoming cell phone debate that is heading towards Westlawn.

Now this is a public forum, so I am not going to get into the specific reasons for this renewed debate, but I think I can safely identify some general misuses of cellphone/ipod technology that is common to this and other schools.

Then I will present some arguments for and against a BAN ON CELLPHONES!!???

I am really torn on this issue. I am a fierce advocate for the utilization of ed. tech. tools in the classroom and school, but I am seeing so many problems in the classrooms because of cellphone use, and I am not seeing many positive uses of the student owned devices. 

1. Cellphones as distraction - receiving texts and receiving updates and notifications from various sights are distracting students. I know that personally when I get pinged with a new notification or email I want to check right away. This is happening in the classrooms and it is making teachers justifiably angry. Listening to music at inappropriate times is also a manifestation of this cellphones as distraction problem.
2. Cellphones as agents of evil - I am so freakin tired of the word bullying, but cellphones are used to be mean to other people. There are all kinds of ways that these adolescents are mean to each other through their phones during the school day. Girls texting each other the mean, profane and threatening things they would never say in person, anonymous sites like ask.fm that allow people to send and receive some of the most hate-filled and vile anonymous messages that I have ever seen. Problems with cameras and sharing inappropriate pictures (take this for what you will, it is a problem in all schools and it needs to be addressed). 
3. Cellphones as underutilized (non-utilized) potential. One of the most provocative and damning arguments here is that they aren't being used anyway, so why have them in the classroom. If the cellphone is only ever used by the teacher as device for listening to music in social and a calculator in math then do students really need their cellphone in class?

The three items above captures the main problems with cellphones in schools and can be used to justify the ban on cellphones at Westlawn. Did I miss any of the big reasons to ban cellphones from our students? Let me know in comments.

Onto the other side of the debate. 

IDK who would argue which side here. Donkey Laugh or Objectivist (both  insults)

Two of the above points can be handled in one argument, and I am not trying to be contrite, but this one argument alone is enough to practically end the debate because of the logical finality of it:

Students need to be taught how to handle and navigate the distractions of their always on, always connected digital environment. Students need to be taught the positive uses of cellphone technology in order to counter the evil that they are currently being taught by society and their peers. Junior high is the time to teach and assess the learning of these skills, values and attitudes.

There, I might as well leave the debate now, that's all that really needs to be said, but of course it isn't. Given that you agree with the above argument you would have to agree that cellphones do in fact belong in the school. They even need to be brought out on purpose, so that they can be discussed and children can be taught how to use them properly. This work is too important, and doing nothing is too destructive, that it can't be left to individual classroom teachers. 

Here is what I propose needs to be done as an alternative to banning cellphones:

1. A curriculum of lessons and assessments teaching students the nature of cellphones and digital technology as agents of good and evil. One or two lessons a month delivered to homeroom classes, so that all students are learning the same lesson together. This would take some thought on how exactly to develop this, but as an example we could run grade 7 - texting, it's impacts and consequences, grade 8 - anonymous messaging, it's impacts and consequences, grade 9 - sending nude pictures, it's impacts and consequences. Some lessons can be delivered to all grades - grade 7, 8 + 9 reporting evil online behaviour: is it tattling? With a well thought out body of lessons we can teach and measure and value the right kind of behaviour, and when society looks at us, or we look at the mistakes our students still make we can at least say that we did teach the lessons and provided that opportunity for students.
2. A whole staff built school policy on the use of cellphones in class. Our current policy, that it is a classroom decision, is flawed. There is a correct time to listen to music, and it is not while you are reading!!!!! Students should know what the consequences will be for breaking policy in all classrooms. One policy that I support is that students are required to show their communication to their teachers when asked. This will be contentious, and considered by some to be an invasion of privacy, but it is necessary if we are the agents that society has deemed responsible for teaching these lessons. Once the policy is agree on, we communicate to students and we communicate to parents, and if they do not agree than the cellphone is, in fact, banned.
3. Teachers need better PD on how to use cellphones for productive work. Remind 101, polleverywhere, how to send pictures to a class blog, and blogging with your phone. Teachers need to be taught that these tools exist, and they need to be taught how to use them with their students.

This blog post helped me think seriously and concisely about the topic. What started as a conflict, now seems very clear to me. One last thought remains only partly expressed. Students will have these devices, it's inevitable. In some families they will be taught how to use them for good and not evil, but in low-income areas like ours, this will not always happen. Our students deserve to learn how to navigate these waters. So often I catch myself saying, "these poors kids, how will they not drown in this sea of change?" Yes, I am often melodramatic at work. They do not come into grade 7 ready equipped with how to survive the digital age, but they should sure as hell leave grade 9 with a few tools to help them on their way.

Descent into the Maelstrom

I am going to borrow heavily from the ideas of Marshall McLuhan here, and I invite you all to stop reading. Do you remember what he said about Edgar Alle Poe's story, Descent into the Maelstrom?

To paraphrase grossly, McLuhan looked at Poe's poem as a metaphor for surviving the chaos of a world that is rapidly changing because of technological change. Here are some excerpts, as you read them (if there is anyone left) think of the storm that this young man and his ship are about to enter as a metaphor for our current situation - rapid technological shift altering the fundamental nature of the world our students are growing up into.

As the boat approaches the Maelstrom:

"I now made one or two attempts to speak to my brother - but, in some manner which I could not understand, the din had so increased that I could not make him hear a single word, although I screamed at the top of my voice in his ear."

 On the inability of our strong and solidly built classroom and schools to weather this new storm:

"When a boat is well built, properly trimmed, and not deep laden, the waves in a strong gale, when she is going large, seem always to slip from beneath her - which appears very strange to a landsman - and this is what is called riding, in sea phrase. Well, so far we had ridden the swells very cleverly ; but presently a gigantic sea happened to take us right under the counter, and bore us with it as it rose - up - up - as if into the sky. I would not have believed that any wave could rise so high."

Can you interpret this passage?
"It may appear strange, but now, when we were in the very jaws of the gulf, I felt more composed than when we were only approaching it. Having made up my mind to hope no more, I got rid of a great deal of that terror which unmanned me at first. I suppose it was despair that strung my nerves."

As educators, we are already in the middle of the storm. We can ignore the noise and clamour of the outside world and focus our attention on helping student survive the storm:
"There was another circumstance which tended to restore my self-possession ; and this was the cessation of the wind, which could not reach us in our present situation - for, as you saw yourself, the belt of surf is considerably lower than the general bed of the ocean, and this latter now towered above us, a high, black, mountainous ridge. If you have never been at sea in a heavy gale, you can form no idea of the confusion of mind occasioned by the wind and spray together. They blind, deafen, and strangle you, and take away all power of action or reflection. But we were now, in a great measure, rid of these annoyances"

The Desire to ban cellphones:
"As I felt the sickening sweep of the descent, I had instinctively tightened my hold upon the barrel, and closed my eyes. For some seconds I dared not open them."

Here is the secret for survival, observation and reflection: We have to help students to observe and reflect. 

"Looking about me upon the wide waste of liquid ebony on which we were thus borne, I perceived that our boat was not the only object in the embrace of the whirl. Both above and below us were visible fragments of vessels, large masses of building timber and trunks of trees, with many smaller articles, such as pieces of house furniture, broken boxes, barrels and staves. I have already described the unnatural curiosity which had taken the place of my original terrors. It appeared to grow upon me as I drew nearer and nearer to my dreadful doom. I now began to watch, with a strange interest, the numerous things that floated in our company. I must have been delirious - for I even sought amusement in speculating upon the relative velocities of their several descents toward the foam below. 'This fir tree,' I found myself at one time saying, 'will certainly be the next thing that takes the awful plunge and disappears,' - and then I was disappointed to find that the wreck of a Dutch merchant ship overtook it and went down before. At length, after making several guesses of this nature, and being deceived in all - this fact - the fact of my invariable miscalculation - set me upon a train of reflection that made my limbs again tremble, and my heart beat heavily once more.

"It was not a new terror that thus affected me, but the dawn of a more exciting hope. This hope arose partly from memory, and partly from present observation."

After observation and reflection:
"I no longer hesitated what to do. I resolved to lash myself securely to the water cask upon which I now held, to cut it loose from the counter, and to throw myself with it into the water. I attracted my brother's attention by signs, pointed to the floating barrels that came near us, and did everything in my power to make him understand what I was about to do. I thought at length that he comprehended my design - but, whether this was the case or not, he shook his head despairingly, and refused to move from his station by the ring-bolt. It was impossible to reach him;"

This storm will not last forever:
"The barrel to which I was attached sunk very little farther than half the distance between the bottom of the gulf and the spot at which I leaped overboard, before a great change took place in the character of the whirlpool. The slope of the sides of the vast funnel became momently less and less steep. The gyrations of the whirl grew, gradually, less and less violent. By degrees, the froth and the rainbow disappeared, and the bottom of the gulf seemed slowly to uprise. The sky was clear, the winds had gone down, and the full moon was setting radiantly in the west, when I found myself on the surface of the ocean, in full view of the shores of Lofoden, and above the spot where the pool of the Moskoe-ström had been"




Another "last thought" on my interpretation of McLuhan. He is often understood as a supporter and advocate of technological change. I disagree with this interpretation. McLuhan was terrified of what electricity and television were doing to humanity. If he were to see the power of the devices that our students carry around today he would think us mad and likely doomed. What McLuhan advocated was awareness and planning. Look at the changes you have wrought! Imagine the future changes that are coming! You must prepare yourself and your society in order to survive with values and sanity intact.

We need to heed his prescient advice and prepare ourselves and our students to survive this and the future of  technological change.

Please comment below.