To see my previous posts, reflecting on sessions 1-4, click on the below links...
Session 1: http://goo.gl/zGhmxD
Session 2-3: http://goo.gl/2pjIQR
Session 4: http://goo.gl/w61q9o
Session 5 of How to Learn Math by @joboaler via Stanford University's online platform (class.stanford.edu) is called 'Conceptual Learning, Part 1: Number Sense'.
The session is possibly the most interesting yet due to the amount of classroom practice you get to see via the videos that are posted in the session. The session begins by calling on recent research to suggest that students' foundational knowledge of mathematics is what determines how successful they are in their future mathematics. Now, I've always been a believer that maths is like a set of building blocks and without the basics you don't get very far; you need a base level in order to build upon.
This is what this session was about. The session looked out how, at the basic level, students count, count on, have knowledge of number bonds or use 'number sense', the ability to break down and move around parts of numbers in order to make arithmetic easier. For example, when adding 7 and 18 you could add 18 and 2 to make 20 and then add on the remaining 5 (from the 7) to make 25. This was one of the examples I was given.
This was when the session got really great...
I was asked to then watch a few teachers going through some 'Number Talks' or 'Math Talks'. These classroom observations were fantastic in showing teachers' methods in finding out students ways of working out multiplications, additions and thinking of basic number questions. The clips showed a class of high school/undergrad students answering questions like 18 x 5, 12 x 15 and 25 x 29.
In each of the clips I was asked to note down what the teacher was doing and the 'teacher moves' they were using in the 'Number Talk'. These alone were really useful in thinking of ways to pull out answers from students, cover mistakes that crop up and get students to really think about how they're explaining their answers. I particularly found it interesting how one teacher used leading questions to drag out clarification from students as to what they were thinking. Lead ins like 'because...' and 'you knew that...' helped to get students to think of ways of explaining their previous thoughts.
What I also liked was that the teachers visualised the problems for students to give an added representation of the problems given. These were then linked to algebra and the distributive/associative laws.
A tip I picked up during the videos was that when a new idea or question was posed the teacher would get students to discuss with one another what they thought, rather than just waiting for someone to respond, as was stated - 'when ideas are complicated or new, sharing ideas can help u clarify our own thinking'.
The best thing about the 'Number Talks' is that it allows you and your peers to see the number of different ways of looking at a problem. It allows you to discuss common misconceptions and cover mistakes (learning from them in the process). For example with the first 18 x 5 question you could:
halve 18 to make 9, multiply this by 5 to give 45 and then double it to get 90
do 10 x 5 and 8 x 5 to get 50 and 40 and then add to give 90
do 20 x 5 to give 100 and then subtract 2 x 5 to give 90
you could visualise the problem in your head as being a multiplication problem set out in 'columns', going through what you carry over at each step and then coming to your answer
you could split the 18 into 6 and 3 and the 9 into 3 and 3 and then multiply these numbers together
you could draw a rectangle with length 18 and width 9, split it up as you feel best and work out individual areas before adding together
and so on and so on.
The beauty with this open approach to seeing the thinking involved is that you don't automatically see ALL possibilities, just the one that you perhaps prefer or know best. So, by getting all answers from a class you get to see other people's thinking and then can approach a new problem with an additional perspective.
I kept hearing phrases like 'number sentence' and 'friendly numbers'. These may be terms they use in the USA more often they we do in the UK, or perhaps they're used in the primary setting more than secondary but I can't say I've come across them myself, until now!
For clarity, a number sentence is a way of working out a problem, so for the problem where students were given a 'dot card' and asked how many dots were on it they were asked to say how they approached the problem. One student said they saw one row of 3, then a row of 2 and then another row of 3 and a final row of 2. Their number sentence would then be 3 + 2 + 3 + 2 = 10.
A 'friendly number' is a number that is 'nicer' to count with, like 10 and 5 and students try to break larger numbers down to these 'friendly numbers' to make the addition/multiplication/division etc easier to do. So for example 16-13 could be 10-10 and then 6-3 to give 3, rather than counting backwards, which requires a more difficult skill.
I continue to really enjoy the course:
it's making me think about the types of tasks I want to focus more heavily on this year
it's getting me to think about the language I use in class
it's getting me to think about the questions I pose in class
it's getting me to think about the messages my classroom can give students
and ultimately it's getting me to think more about how my students learn maths.
The videos are fantastic, the resources and references you can read through the online platform/download are great. I like the peer feedback facility and the short tasks that you are asked to do on there. If anyone hasn't started this already I suggest you sign up - there's plenty of time before the expiry of the course at the end of September.
I'm already getting intrigued about the student version of the course that will be coming out and whether this will be in the same format (online, free, through stanford.edu) and how best to get my students on board with it and signed up! Hopefully more details will come available in due course...?
Tampilkan postingan dengan label HowToLearnMath. Tampilkan semua postingan
Tampilkan postingan dengan label HowToLearnMath. Tampilkan semua postingan
Sabtu, 10 Agustus 2013
Jumat, 09 Agustus 2013
Picture Beads
Inspired by a question I was posed in Jo Boaler's (@joboaler) 'How to Learn Math' free online course [see http://class.stanford.edu] I have been getting creative with 'picture beads'!
Here's the question Jo posed...
This question has 2 parts, 1 open ended (growth-mindset) question and 1 closed (fixed-mindset) question.
The 'How do you see this shape growing' is of course the growth-mindset question as it is open ended, there are multiple answers, multiple entry points for students and there are different ways of looking at the problem (which I personally didn't see at first).
The 'How to Learn Math' course has made me more aware of the types of questions and tasks I give out in class and that I should be trying to make tasks as open ended as possible in order to instill a more growth-mindset in my students, allowing them to learn from their mistakes rather than just going through the methods learnt etc.
So, whilst I was in Ikea with @kutrahmoore (we were looking for a few bits for our new flat, exciting times!) she came across some beads that she apparently wanted to get elsewhere but were too expensive. I had no idea what they were or what she wanted them for but she said she'd explain when we got home.
Here's the pot (£5)...
When we got back...oh, I should probably say now that she's a Design & Technology teacher and so is a bit 'arty farty' having worked at a ceramics studios, studied at London College of Fashion (LCF) etc...she showed me how the beads worked by putting them on a 'peg board' in some sort of fashion, you then iron over the beads and it melts the plastic creating a picture of some sort that you can use for keyrings, place mats etc (I'm sure she'd come up with far more interesting ways of using these crafts).So, it got me thinking of how I could use them. Immediately I thought about the beads and patterns they could form/make and so I started to play around with some of them on one of her peg boards.
Here's what I created...
Here's my beads on the peg board arranged in a few patterns. My thinking is that I'd make a few of these and hand them out in class and pose students the same question as Jo did above...'How do you see this shape growing'. Then we'd go on to looking at working out specific pattern numbers, the 'nth' pattern etc. So, once you've created your pattern you then...
...put a piece of tracing paper (provided with the kit) over it and then carefully (otherwise the little buggers will move and you'll have to start over - this sucks) iron over it melting the plastic and making the beads 'stick' together. You have to iron them for about 3-4 mins and then...
...leave them to cool before peeling them off the peg board and the tracing paper.
This is what they look like when they're finished, although Hannah (@kutrahmoore) said I should have ironed both sides. The side shown is the non-ironed side as I liked how the individual beads are easier to see here (and count). If I'd have ironed both sides you lose a bit of the definition between beads (as they all melt into one).
Naturally, after I had made a few patterns for class I started to experiment...
Then @kutrahmoore gave it a go too...
...and we created these little beauties! Great for a rainy day, or if you're a math teacher looking to introduce some open question on sequences/series/patterns etc.
We then got thinking and thought that these would be a great thing to do in a 'Creative Maths Club' that could be run after school for students to attend. They could take their created patterns home after, or even better, be used in other classes by other students - all created by the students. I've also thought about making some ratio bracelets too to use in class, all I'll need for this is some wire and to thread the beads onto these in different ratios!
Other ideas for a 'Creative Maths Club':
Origami numbers (I recently found an App on the iPhone that gives you instructions for making numbers from origami (folding paper)).
Angry Bird Nets
Polydron 3D shapes
Making Math board games
Darts! (there's a blog post coming soon about this)
+ plenty more
Get some 'picture beads', and the like, by going to Ikea http://www.ikea.com/gb/en/search/?query=pyssla or any other good arts and crafts store!
Here's the question Jo posed...
The 'How do you see this shape growing' is of course the growth-mindset question as it is open ended, there are multiple answers, multiple entry points for students and there are different ways of looking at the problem (which I personally didn't see at first).
The 'How to Learn Math' course has made me more aware of the types of questions and tasks I give out in class and that I should be trying to make tasks as open ended as possible in order to instill a more growth-mindset in my students, allowing them to learn from their mistakes rather than just going through the methods learnt etc.
So, whilst I was in Ikea with @kutrahmoore (we were looking for a few bits for our new flat, exciting times!) she came across some beads that she apparently wanted to get elsewhere but were too expensive. I had no idea what they were or what she wanted them for but she said she'd explain when we got home.
Here's the pot (£5)...
When we got back...oh, I should probably say now that she's a Design & Technology teacher and so is a bit 'arty farty' having worked at a ceramics studios, studied at London College of Fashion (LCF) etc...she showed me how the beads worked by putting them on a 'peg board' in some sort of fashion, you then iron over the beads and it melts the plastic creating a picture of some sort that you can use for keyrings, place mats etc (I'm sure she'd come up with far more interesting ways of using these crafts).Here's what I created...
We then got thinking and thought that these would be a great thing to do in a 'Creative Maths Club' that could be run after school for students to attend. They could take their created patterns home after, or even better, be used in other classes by other students - all created by the students. I've also thought about making some ratio bracelets too to use in class, all I'll need for this is some wire and to thread the beads onto these in different ratios!
Other ideas for a 'Creative Maths Club':
Origami numbers (I recently found an App on the iPhone that gives you instructions for making numbers from origami (folding paper)).
Angry Bird Nets
Polydron 3D shapes
Making Math board games
Darts! (there's a blog post coming soon about this)
+ plenty more
Get some 'picture beads', and the like, by going to Ikea http://www.ikea.com/gb/en/search/?query=pyssla or any other good arts and crafts store!
How to Learn Math (Session 4)
To see my reflections on session 1, and sessions 2 and 3 click on the links below...
session 1 - http://goo.gl/zGhmxD
sessions 2 & 3 - http://goo.gl/2pjIQR
I was looking forward to session 4 ever since Jo Boaler (@joboaler) had started to refer to Carol Dweck's research in fixed and growth-mindsets. Session 4 was titled 'Teaching for a growth mindset'.
As the session title suggests it focused on how you can teach a growth mindset to your students. There was a really great video at the start of the session that got you to look at a teacher in the states introducing the question of what 1 divided by two thirds would be. The lesson was fantastic in showing an approach whereby the students are invited to show their thinking of a problem and trying to make sense of the problem. The 'how does it make sense' part was key to the lesson where the teacher asked her students to show why they thought their answer made sense, rather than showing a method, getting students to learn and copy that method and then apply it to some questions. What I thought was great in the lesson was how many different reasons were presented by the students and how some of these reasons would not have been discussed had the teacher just taught the method to dividing fractions.
In the lesson you had one student draw circles on the board, split them into thirds and then highlighting 2 of the thirds before exclaiming that you have 1 and a half of the two thirds. Another student used a rectangle, like a strip to show how this could be split into 3 equal parts and then used a similar explanation to show an answer of two thirds. There were one or two students who still couldn't grasp these explanations and persisted with an answer of 6 as they believed the 2 over 3 'line' meant that you multiplied the 2 and 3 together. This misconception was picked up by another student (not the teacher) and explained. The same student then randomly pulled out the number 12 when the teacher was putting the question into context of having a yard of wood (or something like that) and needing to take two third chunks from it. The student that mentioned 12 was asked what they meant to which they replied there were 12 feet in a yard. You could almost here the teacher's mind click before she said yes, and what is two thirds of 12? 8 and then you have 4 left over which is half of this, which makes 1 and a half.
These discussions wouldn't have been discussed had the students not been asked to 'make sense' of the problem, rather than just answering it.
Then, in the session, we were asked to look at a blog post from a teacher who had taken a rather closed question involving mini golf and transformed it into a really interesting and engaging open ended task. This was great to read and it is definitely a lesson I'll be using in the future when teaching similar triangles.
Check out www.fawnnguyen.com!
A few tips I picked up throughout the session were to 1) get students to 'convince themselves, convince a friend, convince a skeptic' and to 2) use a 'number sentence' when explaining their reasons to the class.
As has happened in previous sessions we were asked to do a few peer assessment questions which are read and commented on by other subscribers to the course. These questions/feedback have been really useful in seeing what ideas/opinions other teachers have and what things they are planning to do to get across growth-mindset messages to their classes.
The session also looked at what makes a growth-mindset problem and gave us 5 key things the growth mindset question should be (including having multiple entry points and being open). Jo discussed the problems with setting students in mathematics and what messages this gives them. She also discussed what good (growth-mindset) feedback should look like, why grades shouldn't be given based on research conducted and talked about our 'math brain'.
'Remember, the harder you work, the better you get at math'.
Check out www.map.mathshell.org too.
Go to http://class.stanford.edu to sign up for Jo Boaler's 'How to Learn Math' now!
session 1 - http://goo.gl/zGhmxD
sessions 2 & 3 - http://goo.gl/2pjIQR
I was looking forward to session 4 ever since Jo Boaler (@joboaler) had started to refer to Carol Dweck's research in fixed and growth-mindsets. Session 4 was titled 'Teaching for a growth mindset'.
As the session title suggests it focused on how you can teach a growth mindset to your students. There was a really great video at the start of the session that got you to look at a teacher in the states introducing the question of what 1 divided by two thirds would be. The lesson was fantastic in showing an approach whereby the students are invited to show their thinking of a problem and trying to make sense of the problem. The 'how does it make sense' part was key to the lesson where the teacher asked her students to show why they thought their answer made sense, rather than showing a method, getting students to learn and copy that method and then apply it to some questions. What I thought was great in the lesson was how many different reasons were presented by the students and how some of these reasons would not have been discussed had the teacher just taught the method to dividing fractions.
In the lesson you had one student draw circles on the board, split them into thirds and then highlighting 2 of the thirds before exclaiming that you have 1 and a half of the two thirds. Another student used a rectangle, like a strip to show how this could be split into 3 equal parts and then used a similar explanation to show an answer of two thirds. There were one or two students who still couldn't grasp these explanations and persisted with an answer of 6 as they believed the 2 over 3 'line' meant that you multiplied the 2 and 3 together. This misconception was picked up by another student (not the teacher) and explained. The same student then randomly pulled out the number 12 when the teacher was putting the question into context of having a yard of wood (or something like that) and needing to take two third chunks from it. The student that mentioned 12 was asked what they meant to which they replied there were 12 feet in a yard. You could almost here the teacher's mind click before she said yes, and what is two thirds of 12? 8 and then you have 4 left over which is half of this, which makes 1 and a half.
These discussions wouldn't have been discussed had the students not been asked to 'make sense' of the problem, rather than just answering it.
Then, in the session, we were asked to look at a blog post from a teacher who had taken a rather closed question involving mini golf and transformed it into a really interesting and engaging open ended task. This was great to read and it is definitely a lesson I'll be using in the future when teaching similar triangles.
Check out www.fawnnguyen.com!
A few tips I picked up throughout the session were to 1) get students to 'convince themselves, convince a friend, convince a skeptic' and to 2) use a 'number sentence' when explaining their reasons to the class.
As has happened in previous sessions we were asked to do a few peer assessment questions which are read and commented on by other subscribers to the course. These questions/feedback have been really useful in seeing what ideas/opinions other teachers have and what things they are planning to do to get across growth-mindset messages to their classes.
The session also looked at what makes a growth-mindset problem and gave us 5 key things the growth mindset question should be (including having multiple entry points and being open). Jo discussed the problems with setting students in mathematics and what messages this gives them. She also discussed what good (growth-mindset) feedback should look like, why grades shouldn't be given based on research conducted and talked about our 'math brain'.
'Remember, the harder you work, the better you get at math'.
Check out www.map.mathshell.org too.
Go to http://class.stanford.edu to sign up for Jo Boaler's 'How to Learn Math' now!
Jumat, 02 Agustus 2013
How to Learn Math (Sessions 2 & 3)
For my blog post on session 1 of this free online course by @joboaler click here.
Session 2 of the 'How to Learn Math' course I'm currently working my way through was called 'Maths and Mindset' and spoke about how the brain can change and adapt and discussed the differences between a 'fixed' mindset and a 'growth' mindset.
This session was shorter than session 1 and introduced Carol Dweck's mindset research. The session asked a few short questions, the one that stuck out was one where I was asked to say how, if schools took mindset evidence seriously, would things change.
The main way I feel things would need to change is how we, as teachers, give students feedback and how what we say and how students interpret our messages affect their mathematics and attitudes towards maths.
Session 3 was called 'Mistakes and Persistence'. Having introduced the 'fixed' vs 'growth' mindset work in session 2, this session spoke about how students learn best from making mistakes. There was a really interested part about what happens in our brains when we make mistakes, in terms of the synapses etc.
What seemed to be evident from the two sessions is that people with a 'growth' mindset make more mistakes and learn from them. It didn't take long before I realised that this course will help me introduce a 'Fail Safe' culture in my room this year. Session 4, which I am looking forward to, is 'Teaching for a growth mindset'. This session, I hope, will give me strategies to use in class this year to help enforce a 'growth' mindset in my students, make them feel safe in the fact that they can make mistakes without feelings of 'i've failed' or 'i'm not good at maths'.
What also became evident in this session was the subtleties in the language you use in class and how this language affects your students. For example, rather than saying, 'no, that's wrong' saying 'not quite yet' implies that they will, at some point get to the correct answer and are on a 'learning journey' towards that end; making a few mistakes along the way and learning from them.
Another interesting point was that of the 'didactic contract'. The contract we enter into with students when asked for help. A student will put up their hand and ask a question and the teacher would go over, answer the question for the student, and then the student has the answer they sought, without any real thinking on their behalf. As much as I'd like to say that I, instead, encourage students to seek the answers themselves by asking other questions of them like 'what have you tried so far', 'what do you think you could do', 'if you tried 'x' and it didn't work, how about trying 'y'?' and so on. This is something that naturally, when you're a bit fed up, it's the end of the week (perhaps Friday P5) and the student in question is short on interest, becomes easier to give them the answer they seek in the hope that they then apply your thinking (from your explanation to them when telling them the answer) to the next question.
Finally, there was a discussion on speed in mathematics lessons and how this is one of the contributing factors to students experiencing anxiety in our subject and being afraid to make mistakes. This even included questioning timed examinations and whether the time it takes a person to complete a task is really important over them arriving at the answer/solution in their own time. The pressure time can put on students to complete tasks got me to think about the timings I give in class, the 1 min timed times tables task I have given my 'bottom set' students all year and whether this has had a detrimental effect on their progress/mindset.
However, we need to have some time constraints surely? So, I perhaps need to do a bit more thinking here. Project-based learning tasks clearly are open to the amount of time a student spends on them, but there needs to be a point where we say, 'OK, that's done now and lets move on'. I feel that in class, timed tasks can increase students motivation, especially if there is a competitive element to the task?
As the last task in session 3 we were asked to design a poster to state to students that they learn from their mistakes and that it was OK to make them. I've recently purchased the 'Fail Safe' posters from @SparkyTeaching (http://www.sparkyteaching.com/resources/creative/failsafe.php) as part of my want to create a more 'mistakes are ok' environment this year. I gave the link to these posters for this task as I think they're great.
In summary (and things for me to think about/do):
'growth' mindsets beat 'fixed' mindsets hands down
I've got to get students into this 'growth mindset'
mistakes are important and are huge learning opportunities
'didactic contract' - avoid it
speed (good or bad?) - 'faster isn't smarter'
think about the language used in class
effort is needed from the students to solve a problem that is challenging
set up more 'Spot the Mistake' plenaries
think about feedback given in books/verbally
'I love mistakes'
students write mistakes on board and discuss as a class
Right, off to do session 4...
Session 2 of the 'How to Learn Math' course I'm currently working my way through was called 'Maths and Mindset' and spoke about how the brain can change and adapt and discussed the differences between a 'fixed' mindset and a 'growth' mindset.
This session was shorter than session 1 and introduced Carol Dweck's mindset research. The session asked a few short questions, the one that stuck out was one where I was asked to say how, if schools took mindset evidence seriously, would things change.
The main way I feel things would need to change is how we, as teachers, give students feedback and how what we say and how students interpret our messages affect their mathematics and attitudes towards maths.
Session 3 was called 'Mistakes and Persistence'. Having introduced the 'fixed' vs 'growth' mindset work in session 2, this session spoke about how students learn best from making mistakes. There was a really interested part about what happens in our brains when we make mistakes, in terms of the synapses etc.
What seemed to be evident from the two sessions is that people with a 'growth' mindset make more mistakes and learn from them. It didn't take long before I realised that this course will help me introduce a 'Fail Safe' culture in my room this year. Session 4, which I am looking forward to, is 'Teaching for a growth mindset'. This session, I hope, will give me strategies to use in class this year to help enforce a 'growth' mindset in my students, make them feel safe in the fact that they can make mistakes without feelings of 'i've failed' or 'i'm not good at maths'.
What also became evident in this session was the subtleties in the language you use in class and how this language affects your students. For example, rather than saying, 'no, that's wrong' saying 'not quite yet' implies that they will, at some point get to the correct answer and are on a 'learning journey' towards that end; making a few mistakes along the way and learning from them.
Another interesting point was that of the 'didactic contract'. The contract we enter into with students when asked for help. A student will put up their hand and ask a question and the teacher would go over, answer the question for the student, and then the student has the answer they sought, without any real thinking on their behalf. As much as I'd like to say that I, instead, encourage students to seek the answers themselves by asking other questions of them like 'what have you tried so far', 'what do you think you could do', 'if you tried 'x' and it didn't work, how about trying 'y'?' and so on. This is something that naturally, when you're a bit fed up, it's the end of the week (perhaps Friday P5) and the student in question is short on interest, becomes easier to give them the answer they seek in the hope that they then apply your thinking (from your explanation to them when telling them the answer) to the next question.
Finally, there was a discussion on speed in mathematics lessons and how this is one of the contributing factors to students experiencing anxiety in our subject and being afraid to make mistakes. This even included questioning timed examinations and whether the time it takes a person to complete a task is really important over them arriving at the answer/solution in their own time. The pressure time can put on students to complete tasks got me to think about the timings I give in class, the 1 min timed times tables task I have given my 'bottom set' students all year and whether this has had a detrimental effect on their progress/mindset.
However, we need to have some time constraints surely? So, I perhaps need to do a bit more thinking here. Project-based learning tasks clearly are open to the amount of time a student spends on them, but there needs to be a point where we say, 'OK, that's done now and lets move on'. I feel that in class, timed tasks can increase students motivation, especially if there is a competitive element to the task?
As the last task in session 3 we were asked to design a poster to state to students that they learn from their mistakes and that it was OK to make them. I've recently purchased the 'Fail Safe' posters from @SparkyTeaching (http://www.sparkyteaching.com/resources/creative/failsafe.php) as part of my want to create a more 'mistakes are ok' environment this year. I gave the link to these posters for this task as I think they're great.
In summary (and things for me to think about/do):
'growth' mindsets beat 'fixed' mindsets hands down
I've got to get students into this 'growth mindset'
mistakes are important and are huge learning opportunities
'didactic contract' - avoid it
speed (good or bad?) - 'faster isn't smarter'
think about the language used in class
effort is needed from the students to solve a problem that is challenging
set up more 'Spot the Mistake' plenaries
think about feedback given in books/verbally
'I love mistakes'
students write mistakes on board and discuss as a class
Right, off to do session 4...
Selasa, 30 Juli 2013
How to Learn Math - Introduction (Session 1)
Having seen a few things floating around twitter and on the TES Mathematics community blog (http://community.tes.co.uk/tes_mathematics/b/weblog/default.aspx) I have enrolled today on Jo Boaler's 'How to Learn Math' course on Stanford University's free online platform.
All the course details are found on this site:
https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about
Registration is really simple and you can start the course whenever you like and work through the 8 sessions at your own pace. It started on the 15th July and runs to the 27th Sep (2013). I've only just enrolled but haven't missed anything - all the course content for each session is ready to go once you've signed up.
Follow Jo Boaler on Twitter @joboaler and use the hashtag #HowToLearnMath to communicate with others on the course (there's over 25,000 people signed up to it).
I've just finished working my way through Session 1 (Introduction) and here are my thoughts so far...
The first session introduced the course and explored the problems with Mathematics teaching, perceptions about the subject and stereotypes behind the subject and its' learners. The main thing I have taken away from the session is just how much negativity there is towards our subject and how this can be combated by us teachers and the parents of our students too.
Throughout the session you are presented with a series of videos and complementing exercises to fill in/complete. These are fairly short exercises but can take longer depending on how much time you have to give to the course. I like the element of peer feedback where you are able to see others' responses and comment on them.
Personally it has made me think about how I teach Mathematics and what presumptions and generalisations I make about my students. It also made me question why so many students come into secondary school with a negative feeling towards Mathematics. Some students seem to have this perception that Mathematics is hard, they're not 'good at maths' and aren't as good as others. The session discussed the gender stereotypes in Mathematics and other cultural influences.
It got me thinking about how we 'label' some students in Mathematics, especially those 'bottom set' students who already find mathematics difficult but then get labelled as the 'bottom set' and this just helps to reinforce their beliefs. This, I feel, is one of the biggest problems with ability-setting students - the fact we attach some sort of label of ability to these students. I too am guilty of this as I can recall many times where I have, on my blog, referred to my 'bottom set' students as 'low ability'. Are they really? Perhaps, but surely by referring to them in this way I am putting a ceiling on what they are possibly capable of.
There have been lessons this year with these groups where a student may have said something negative to another student following a contribution of theirs to a class discussion. Something along the lines of 'that's wrong you idiot'. This then gets followed up by a comment from this student along the lines of 'well you're in the same set as me, you're just as stupid - we're all set 5!'
How we can move away from this 'label' the students seem to carry around with them is, I suppose, the 'big' question. One which I don't yet have an answer for, but am hoping to try and overcome with these classes.
The session also discussed intervention strategies that had been used to help overcome these stereotypes. These strategies are all psychological, which for me personally is great, what with my Psychology degree and background. The fact that girls can underperform on a test, that they have beforehand marked their gender, emphasises that there are elements of stereotyping that have been embedded in their beliefs and attitudes towards certain subjects.
Something that Craig Barton @mrbartonmaths and @tesMaths stated in his summary of session 1 is that we've all had parents at parents' evening excuse their child's perceived ability in Mathematics or progress in the subject due to them being 'poor' at maths themselves. I feel this is the starting point of students believing that they too can't be good at the subject, or that it is bound to be difficult. I don't think they'll be a student in my classes in September that doesn't have some sort of preconceived idea of their 'worth' in Mathematics. Past experiences will govern whether they are capable, or not, in Mathematics and they may have put them off altogether. Some may have high expectations on them due to always being in 'set 1' or because their parents were good at maths and so they should be too.
All of these questions/thoughts have been brought about by session 1 and the questions Jo poses in the video clips. There are loads of resources as part of the online platform too and I have the rest of Paul Lockhart's 'A Mathematician's Lament' to read (I've read the required first 5 pages) as part of the course reading.
I'm thoroughly looking forward to the rest of the sessions, which I will blog about as and when I complete each one.
I highly recommend this to any Mathematics teacher, teacher, parent or anyone that has some spare time over the Summer who has an interest in the above.
I have also just ordered Jo's book 'The Elephant in the Classroom' too to add to my Summer reading. Available from Amazon (other online book retailers are available of course) at: http://www.amazon.co.uk/The-Elephant-Classroom-Helping-Children/dp/0285638750/ref=sr_1_1?ie=UTF8&qid=1375188955&sr=8-1&keywords=the+elephant+in+the+classroom
All the course details are found on this site:
https://class.stanford.edu/courses/Education/EDUC115N/How_to_Learn_Math/about
Registration is really simple and you can start the course whenever you like and work through the 8 sessions at your own pace. It started on the 15th July and runs to the 27th Sep (2013). I've only just enrolled but haven't missed anything - all the course content for each session is ready to go once you've signed up.
Follow Jo Boaler on Twitter @joboaler and use the hashtag #HowToLearnMath to communicate with others on the course (there's over 25,000 people signed up to it).
I've just finished working my way through Session 1 (Introduction) and here are my thoughts so far...
The first session introduced the course and explored the problems with Mathematics teaching, perceptions about the subject and stereotypes behind the subject and its' learners. The main thing I have taken away from the session is just how much negativity there is towards our subject and how this can be combated by us teachers and the parents of our students too.
Throughout the session you are presented with a series of videos and complementing exercises to fill in/complete. These are fairly short exercises but can take longer depending on how much time you have to give to the course. I like the element of peer feedback where you are able to see others' responses and comment on them.
Personally it has made me think about how I teach Mathematics and what presumptions and generalisations I make about my students. It also made me question why so many students come into secondary school with a negative feeling towards Mathematics. Some students seem to have this perception that Mathematics is hard, they're not 'good at maths' and aren't as good as others. The session discussed the gender stereotypes in Mathematics and other cultural influences.
It got me thinking about how we 'label' some students in Mathematics, especially those 'bottom set' students who already find mathematics difficult but then get labelled as the 'bottom set' and this just helps to reinforce their beliefs. This, I feel, is one of the biggest problems with ability-setting students - the fact we attach some sort of label of ability to these students. I too am guilty of this as I can recall many times where I have, on my blog, referred to my 'bottom set' students as 'low ability'. Are they really? Perhaps, but surely by referring to them in this way I am putting a ceiling on what they are possibly capable of.
There have been lessons this year with these groups where a student may have said something negative to another student following a contribution of theirs to a class discussion. Something along the lines of 'that's wrong you idiot'. This then gets followed up by a comment from this student along the lines of 'well you're in the same set as me, you're just as stupid - we're all set 5!'
How we can move away from this 'label' the students seem to carry around with them is, I suppose, the 'big' question. One which I don't yet have an answer for, but am hoping to try and overcome with these classes.
The session also discussed intervention strategies that had been used to help overcome these stereotypes. These strategies are all psychological, which for me personally is great, what with my Psychology degree and background. The fact that girls can underperform on a test, that they have beforehand marked their gender, emphasises that there are elements of stereotyping that have been embedded in their beliefs and attitudes towards certain subjects.
Something that Craig Barton @mrbartonmaths and @tesMaths stated in his summary of session 1 is that we've all had parents at parents' evening excuse their child's perceived ability in Mathematics or progress in the subject due to them being 'poor' at maths themselves. I feel this is the starting point of students believing that they too can't be good at the subject, or that it is bound to be difficult. I don't think they'll be a student in my classes in September that doesn't have some sort of preconceived idea of their 'worth' in Mathematics. Past experiences will govern whether they are capable, or not, in Mathematics and they may have put them off altogether. Some may have high expectations on them due to always being in 'set 1' or because their parents were good at maths and so they should be too.
All of these questions/thoughts have been brought about by session 1 and the questions Jo poses in the video clips. There are loads of resources as part of the online platform too and I have the rest of Paul Lockhart's 'A Mathematician's Lament' to read (I've read the required first 5 pages) as part of the course reading.
I'm thoroughly looking forward to the rest of the sessions, which I will blog about as and when I complete each one.
I highly recommend this to any Mathematics teacher, teacher, parent or anyone that has some spare time over the Summer who has an interest in the above.
I have also just ordered Jo's book 'The Elephant in the Classroom' too to add to my Summer reading. Available from Amazon (other online book retailers are available of course) at: http://www.amazon.co.uk/The-Elephant-Classroom-Helping-Children/dp/0285638750/ref=sr_1_1?ie=UTF8&qid=1375188955&sr=8-1&keywords=the+elephant+in+the+classroom
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