I've been teaching the same concept with each of my groups - always starting with my Einsteins and moving up the groups. This has illustrated to me the misconceptions in all topics I'm teaching, as well as making me think the concepts through more carefully. Not that I'm spending longer in the planning stage - actually less time, probably.
I've also found that the ARBs have really good conceptual explanations as well as analytical tests, which I will look into further.
Sunday, September 6, 2009
Critical Friend Visit
Liz came to watch me teach my Einsteins where fractions fit on the numberline. I asked her to contribute, rather than just sit back and watch.
What a fascinating session. Students were all prepared to state their ideas, and were adamant about their answers. I asked them to draw a numberline from 1 - 10 in their books and show where 1/2 fitted. They pretty much pointed to 5. Interesting already. It took much coercion, the use of folding paper in half, discussion about what '1' meant, whether 1/2 was more or less than 1. Liz suggested that the paper could represent a chocolate bar. What would Paris prefer 1/2 or 1 whole chocolate bar? The penny finally dropped.
I think it would have been easy to tell them where 1/2 was on the numberline, but the deep understanding was gained.
I did the same lesson with my next group up - Archimedes. They grasped the concept much more quickly, but they still started thinking 1/2 was where 5 was.
Even when I did it with my nearly top Fibonacci group, there was still some teaching to do. You can't ever assume kids have that basic conceptual understanding. One girl, who is in the Explorers group was convinced that 1/2 was less than one. Not that it took long to change her mind, but it illustrated that all kids have misconceptions.
What a fascinating session. Students were all prepared to state their ideas, and were adamant about their answers. I asked them to draw a numberline from 1 - 10 in their books and show where 1/2 fitted. They pretty much pointed to 5. Interesting already. It took much coercion, the use of folding paper in half, discussion about what '1' meant, whether 1/2 was more or less than 1. Liz suggested that the paper could represent a chocolate bar. What would Paris prefer 1/2 or 1 whole chocolate bar? The penny finally dropped.
I think it would have been easy to tell them where 1/2 was on the numberline, but the deep understanding was gained.
I did the same lesson with my next group up - Archimedes. They grasped the concept much more quickly, but they still started thinking 1/2 was where 5 was.
Even when I did it with my nearly top Fibonacci group, there was still some teaching to do. You can't ever assume kids have that basic conceptual understanding. One girl, who is in the Explorers group was convinced that 1/2 was less than one. Not that it took long to change her mind, but it illustrated that all kids have misconceptions.
Conceptualising Maths
I've decided to redirect my Maths Inquiry. More and more I've been thinking about how kids will learn and retain their skills and understandings only if the basic concepts are grasped firmly. These are the basis for all further learning - and not just in Maths. I've been finding my bottom (Einstein) group to be excellent teachers. I'm working very deliberately, and with plenty of materials, and little book recording to give them basic fractions understanding. It's really enjoyable to watch the lights slowly switch on. They've taught me that I need to proceed slowly, but with plenty of activity and sound questioning.
Sunday, August 16, 2009
Teaching Observation
Dinah and the other Skyscraper teachers observed me taking a Maths problem solving session with my 'Einsteins'. Dinah had a really good suggestion - of getting the kids to think of their answer and hold out a certain number of fingers behind their back and then bring their hands forward at the same time. This worked pretty well - but clearly only suited to numbers less than 10. More recently I've really worked to try to get students to feel secure enough to say their answer even when it is different from the others'.
Problem Solving
I have back copies from Mathex - many good and interesting problems to solve. I've put them on our Room 13 Website.
I thought I could be really clever and put the answers in white, thereby making them invisible until I was ready to reveal them. Clever kids discovered them when they dragged the mouse across the apparently empty space!
Much good discussion followed, but I really need to work with my Stage 5 kids who really struggle with basic Maths conceptualisation. This is becoming a priority. It is in my plan, but I think this is central to all Maths understanding. While kids can learn how to do things, they won't be able to apply their skills to other areas without the deep understanding. This certainly applies to all of learning.
Some kids just need practice at solving problems, while others need to learn how.
I thought I could be really clever and put the answers in white, thereby making them invisible until I was ready to reveal them. Clever kids discovered them when they dragged the mouse across the apparently empty space!
Much good discussion followed, but I really need to work with my Stage 5 kids who really struggle with basic Maths conceptualisation. This is becoming a priority. It is in my plan, but I think this is central to all Maths understanding. While kids can learn how to do things, they won't be able to apply their skills to other areas without the deep understanding. This certainly applies to all of learning.
Some kids just need practice at solving problems, while others need to learn how.
POD Meeting
We all shared our Inquiry plans with every other individual pea. This was a good way to refine and re-think. Karleen's inquiry is about unpacking the maths from the word problem. This strikes me as something I also need to do.
Dinah's Session about Open Ended Maths and Problem Solving
What did I get out of this? The idea of open ended Maths suits me - and probably the students because the outcome is not pre-ordained, so it means that all levels can be catered for and challenged.
We were also given a scrap book to collect Maths problem and Open ended Maths ideas in. I'd prefer a digital version, so I may change that, but it's useful for some old Nick Reed hand-written Maths problems.
We were also given a scrap book to collect Maths problem and Open ended Maths ideas in. I'd prefer a digital version, so I may change that, but it's useful for some old Nick Reed hand-written Maths problems.
What's Happened So Far
Inquiry plan to Matt
Survey Monkey Questionnaire
Great session with Dinah, about problem solving and open ended questions. Started a scrap book of ideas.
POD meeting to share and refine our plan.
First critical friend visit (didn't happen for me - I was friendless)
Problem Solving page (on Room 13 Website)
Videoing our teaching, sharing and discussion
Critical Friend Visit by Liz
Survey Monkey Questionnaire
Great session with Dinah, about problem solving and open ended questions. Started a scrap book of ideas.
POD meeting to share and refine our plan.
First critical friend visit (didn't happen for me - I was friendless)
Problem Solving page (on Room 13 Website)
Videoing our teaching, sharing and discussion
Critical Friend Visit by Liz
Survey
Time to set up my Inquiry blog and record what has happened so far.
Here are the results of the survey about current attitudes to Maths:
Interestingly the kids all see themselves as being OK or good at Maths. This must be a good thing because they need to have good self esteem to progress. Most of the class enjoys Maths usually or always. Fantastic!
The Basic Facts Ladder is perceived as being helpful. Although Dinah Harvey suggests it shouldn't be done in maths learning time, my observation is that it is highly motivational. Kids like to know they're improving at something and the ladder provides for that.
Another notable result is the lack of students who don't know if the modeling books and FIOs are helpful. We use modelling books, but seldom use FIOs. I've noted in my Inquiry plan that I should make better use of them to allow kids to get used to the link between literacy and number - as per PAT tests.
Here are the results of the survey about current attitudes to Maths:
Interestingly the kids all see themselves as being OK or good at Maths. This must be a good thing because they need to have good self esteem to progress. Most of the class enjoys Maths usually or always. Fantastic!
The Basic Facts Ladder is perceived as being helpful. Although Dinah Harvey suggests it shouldn't be done in maths learning time, my observation is that it is highly motivational. Kids like to know they're improving at something and the ladder provides for that.Another notable result is the lack of students who don't know if the modeling books and FIOs are helpful. We use modelling books, but seldom use FIOs. I've noted in my Inquiry plan that I should make better use of them to allow kids to get used to the link between literacy and number - as per PAT tests.
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