Workshop 1 | K-2 Click Here for Slides
This workshop focuses on the development of number sense.
We saw the fundamental of counting - same nouns, renaming when nouns are different.
We saw the use of ten frames in counting and also the difference between proportionate and non-proportionate materials. Participants offered the progression for counting - (1) real things before manipulative (2) single nouns before multiple nouns (3) proportionate before non-proportionate.
We saw the use of ten frames, number bonds and visual models to develop number sense.
For addition, we studied the case of single-digit addition and for subtraction, we saw multi-digit subtraction. We also saw an example of a lesson that focused on practice and how the advanced learners are challenged. Struggling learners get support from (1) concrete materials (2) time to figure out (3) working with friends.
Reflection Task | How does the make a shape using four tiles develop number sense?
Workshop 2 | slides are in the same Album as above.
The focus was on multiplicative structures for young children.
We looked at readiness for teen numbers as well as a strong concept in counting in single / two nouns. We also looked at comparing groups and making equal groups.
The main case study looked at variation of problems used in multiplication where we go from both factors represented using physical representations, to only one of the factors represented physically to both factors represented symbolically across four lessons.
Thursday, December 11, 2014
Saturday, December 6, 2014
Anglo Singapore International School | Bangkok
Teachers Session | Click Here for a summary of the discussion on differentiated instruction using a common task.
We learn how to differentiate instruction using an open task as well as differentiated instruction using a basic skill practice tasks.
Make a list of strategies for advanced learners and a list of strategies to support struggling learners.
Three stages of a maths lesson. Four things teachers do to help acquisition and refinement of knowledge. Five things advanced children can do.
How does anchor task and guided practice promotes DI?
How does the use of a journal consistent with DI?
How is asking for more than one method a DI strategy?
How does concrete materials and visuals help?
How does the extended time with one task (anchor task) help?
How does collaborative learning help?
Parents Session | Click Here for two of my list of Big Fives.
Five things advanced children can do. Five core competencies in mathematics.
We learn how to differentiate instruction using an open task as well as differentiated instruction using a basic skill practice tasks.
Make a list of strategies for advanced learners and a list of strategies to support struggling learners.
Three stages of a maths lesson. Four things teachers do to help acquisition and refinement of knowledge. Five things advanced children can do.
How does anchor task and guided practice promotes DI?
How does the use of a journal consistent with DI?
How is asking for more than one method a DI strategy?
How does concrete materials and visuals help?
How does the extended time with one task (anchor task) help?
How does collaborative learning help?
Parents Session | Click Here for two of my list of Big Fives.
Five things advanced children can do. Five core competencies in mathematics.
Wednesday, December 3, 2014
Friday, November 28, 2014
Alkem Professional Development
Saturday, November 22, 2014
Taipei American School 2
This is my second entry. Colleagues at TAS, please Aldo look at the entry just before this to access the various sessions we did with the seven grade level teams.
One theme that surfaced throughout the week is how we challenge our advanced learners. I have put in things for us to observe during the week.
Did you see ...
some KA students were asked to count more than four tiles. At least one of them was asked to add three one-digit numbers. Those are examples of acceleration. But I did those in the context of common activities - everyone was playing with tiles, making stuff and later doing the same coloring activity.
Did you also see ...
Kindergarten students being asked to use 32 cubes to make three numbers, each greater than 10 and them to compare the numbers pairwise . Is that a challenge in itself?
Did you see how groups that completed the job earlier were asked, the three numbers are the same now, can we make them different. Or the three numbers are different, can we make them the same.
Did you also see advanced learners
investigating if there were any relationship between numver of ways to make the equation a + b = n and the value of n, while the class work on finding a and b. N = 12 for this lesson. Did you see students who are capable putting patterns they saw into words? Dud you see them learning to use what their friends did or said to construct their own understanding?
Are all these important?
Did you see advanced learners
using 35 + 55 = 90 to generate equations that met the given conditions that the digits in the addends are different. Did you see the second graders doing things that you think are important for them to learn to do? Make a list of these things. These are your answers to parents who clam our for acceleration.
Not that you did not see acceleration. Did you see Grade 1 went on to do 99 + 3 in a lesson where the girl is to add 1, 2 or 3 to another one-digit numver. The lesson started with 9 + 3. Did you see while other students merely counted on to get 102, advanced learners were saying things test made you proud they are your students? What are those things that they say. Write them down because these are the things you show parents of these kids when they say their children are not challenged enough.
Did you see I end lessons by asking what made you proud today? What challenged you today? What did you learn today?
Diid you see third graders solepce a challenging problem?
Jon folded paper stars. Each day he folded two more than the day before. In seven days, he folded 91 paper stars. The class found that he folded 7 on the first days.
Did you hear
a student suggested that the number in the first day cannot be an even number.
Did you see another suggested doing 91 divided by 7 and use the quotient 13 to get the number folded on the first day.
Did you see advanced learners not able to, initially anyway, not able to use the piece if paper to help them represent a linear equation. Did you see them posing more difficult equations in their design homework for your patents task? The rest were making up x + 1 = 12 while they wrote 2 x x = 12 and were told the xpconvention if leaving out multiplication sign in two times x.
Did you see the advanced learners from 5X learning to articulate their thinking and were pushed to say how a game is not fair and how to make it fair. Dud you see how advanced learners were challenged in the lesson although the whole class were working on the same task - playing a roll a dice game and the deciding where to place the digit in their _ _ _ _ _
Did you see advanced students having fun doing the lesson? Learning more content is fine but have they learn to enjoy what they do. If not that must be learnt before they are accelerated. Acceleration is fine. But let's do that after 'what counts' have been done well.
Did you see?
One theme that surfaced throughout the week is how we challenge our advanced learners. I have put in things for us to observe during the week.
Did you see ...
some KA students were asked to count more than four tiles. At least one of them was asked to add three one-digit numbers. Those are examples of acceleration. But I did those in the context of common activities - everyone was playing with tiles, making stuff and later doing the same coloring activity.
Did you also see ...
Kindergarten students being asked to use 32 cubes to make three numbers, each greater than 10 and them to compare the numbers pairwise . Is that a challenge in itself?
Did you see how groups that completed the job earlier were asked, the three numbers are the same now, can we make them different. Or the three numbers are different, can we make them the same.
Did you also see advanced learners
investigating if there were any relationship between numver of ways to make the equation a + b = n and the value of n, while the class work on finding a and b. N = 12 for this lesson. Did you see students who are capable putting patterns they saw into words? Dud you see them learning to use what their friends did or said to construct their own understanding?
Are all these important?
Did you see advanced learners
using 35 + 55 = 90 to generate equations that met the given conditions that the digits in the addends are different. Did you see the second graders doing things that you think are important for them to learn to do? Make a list of these things. These are your answers to parents who clam our for acceleration.
Not that you did not see acceleration. Did you see Grade 1 went on to do 99 + 3 in a lesson where the girl is to add 1, 2 or 3 to another one-digit numver. The lesson started with 9 + 3. Did you see while other students merely counted on to get 102, advanced learners were saying things test made you proud they are your students? What are those things that they say. Write them down because these are the things you show parents of these kids when they say their children are not challenged enough.
Did you see I end lessons by asking what made you proud today? What challenged you today? What did you learn today?
Diid you see third graders solepce a challenging problem?
Jon folded paper stars. Each day he folded two more than the day before. In seven days, he folded 91 paper stars. The class found that he folded 7 on the first days.
Did you hear
a student suggested that the number in the first day cannot be an even number.
Did you see another suggested doing 91 divided by 7 and use the quotient 13 to get the number folded on the first day.
Did you see advanced learners not able to, initially anyway, not able to use the piece if paper to help them represent a linear equation. Did you see them posing more difficult equations in their design homework for your patents task? The rest were making up x + 1 = 12 while they wrote 2 x x = 12 and were told the xpconvention if leaving out multiplication sign in two times x.
Did you see the advanced learners from 5X learning to articulate their thinking and were pushed to say how a game is not fair and how to make it fair. Dud you see how advanced learners were challenged in the lesson although the whole class were working on the same task - playing a roll a dice game and the deciding where to place the digit in their _ _ _ _ _
Did you see advanced students having fun doing the lesson? Learning more content is fine but have they learn to enjoy what they do. If not that must be learnt before they are accelerated. Acceleration is fine. But let's do that after 'what counts' have been done well.
Did you see?
Monday, November 17, 2014
Taipei American School
Reflection | How giving students time to figure things out is important before discussing difficult ideas. We saw how some students in grade 1 were able to see that the number of equations for ? + ? = n is (n + 1) ways, We saw how students in grade 3 were able to solve this problem - Jon folded paper stars. Each day he folded two more than the day before. In seven days, he folded 91 paper stars. The class found that he folded 7 on the first days. Along the way a student suggested that the number in the first day cannot be an even number. Another suggested doing 91 divided by 7 and use the quotient 13 to get the number folded on the first day. All very high level thinking for grade 1 and grade 3 students. I encouraged teachers in the school to use anchor tasks to organize their mathematics lessons.
Discussion Materials
Teaching Place Values 1 | Click Here
Grade 5 Lesson | Click Here We did comparing decimals and whole numbers.
Grade 4 Lesson | Click Here We did solving linear equations.
Grade 3 Lesson | Click Here and Here We did word problem solving.
Grade 2 Lesson |Click Here We did addition of two digit numbers using mental strategies.
Grade 1 Lesson | Click Here We did adding 1, 2 or 3 to another whole number.
Grade K Lesson | Click Here We did comparing three numbers.
Grade Kindergarten A Lesson | Click Here We did a play activity and a drawing activity while focusing on counting to four things in a set.
Singapore Standards for K | Click Here
Where to check out Ten Frames | Didax and EAI Education
Reference Materials
Struggles | Click Here
Another article on Struggles |Click Here
Discussion Materials
Teaching Place Values 1 | Click Here
Grade 5 Lesson | Click Here We did comparing decimals and whole numbers.
Grade 4 Lesson | Click Here We did solving linear equations.
Grade 3 Lesson | Click Here and Here We did word problem solving.
Grade 2 Lesson |Click Here We did addition of two digit numbers using mental strategies.
Grade 1 Lesson | Click Here We did adding 1, 2 or 3 to another whole number.
Grade K Lesson | Click Here We did comparing three numbers.
Grade Kindergarten A Lesson | Click Here We did a play activity and a drawing activity while focusing on counting to four things in a set.
Singapore Standards for K | Click Here
Where to check out Ten Frames | Didax and EAI Education
Reference Materials
Struggles | Click Here
Another article on Struggles |Click Here
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