We were fortunate because we were able to do our lesson with the entire class. One advantage is that we were able to get more feedback. Another advantage is that I experienced the difference in classroom management from a smaller group compared to the entire class. I had a bit of difficulty getting everyones attention at the end. This showed me that I must be more assertive and speak louder, and simply waiting does not work.
We decided to do a jigsaw activity and one major advantage I realized is that it takes the pressure off the teacher. Rather than the teacher having to plan a lesson covering all the material, the students take over the teacher role and teach each other. The teacher still should walk around and engage with students but it was nice to have a break. Also, the students are more actively listening and learning at each group. They knew they had to go back to their triad and teach the others so this caused them to pay attention.
We should have allowed more time at the end for them to teach each other. We received a few comments on the feedback sheet stating there was not enough time here.
One area on the feedback sheet we received a low mark was connecting our topic to other areas of math. We perhaps could have brought this topic more broad and tied in other ideas.
We had many positive comments about using history (Babylonian, Greek), visuals (ancient tablet, cuneiform script) and relating to real like (base 60 numbering system). I really enjoy history and I worry with a lesson like this because some people find it dry, but I was pleased to see that some comments said that we made a dry topic interesting.
An area I could improve with my group was to involve everyone more since my structure was more lecture type than the other two. I asked for volunteer and when people hesitated I hesitated too! I should have had thought of a different method of engaging them if no one volunteered.
Overall, I am really pleased with out micro-teaching lesson. I have only seen this jigsaw activity in my other classes with humanities related topics or reading. I see now that this can work in a math class. But I must remember that there will not be 3 teachers.
Saturday, October 16, 2010
Thursday, October 14, 2010
Group Micro Teaching – Apprenticeship and Workplace 10
Bridge: 2 min
Catch interest by having students form groups of three and numbering themselves 1,2,3 for jigsaw activity in which they will become the expert on some aspect of the history or modern use of the Pythagorean Theorem.
Learning Objective:
Students will be able to demonstrate an understanding of the Pythagorean Theorem by describing historical and contemporary applications of it.
> To learn a historical use for Pythagorean Theorem and to understand where Pythagoras' inspiration came from.
> To understand that this theorem came about from a practical application, not pen and paper theory.
Teaching Objective:
> Learn and improve our methods in conducting an engaging and educational lesson that will reach everyone.
> To interactively show the motivation for the Pythagoras Theorem, introduced to Pythagoras by the ancient Egyptians.
> To try out the Jigsaw strategy.
Pre-test: 1 min
> Who can tell me what we already know about the Pythagorean Theorem?
o Looking for formula, triples, and to see if anyone might already know where it comes from.
Participatory Learning: 7 min
> Split groups into 1’s, 2’s and 3’s.
o 1’s at Egyptian Station (Deb)
o 2’s at Babylonian Station (Michelle)
o 3’s at Modern Application Station (Nadine)
Station 1 – Egyptians
> Explain how ancient Egyptians used a right-triangle to redistribute fields after yearly flooding.
> Explain how they made a right triangle using rope and knots
> Explain how Pythagoras became involved/interested
> Make a right-triangle with a piece of string and ruler. Make a 3, 4, 5 triangle and see if they can find a right angle in the classroom with it.
Station 2 – Babylonians
> Explain Babylonian Mathematics and history of Pythagorean Theorem.
> Teaching Babylonian numbering system and ancient tablet.
> Briefly cover other ancient cultures in which Pythagorean Theorem was known and used
Station 3 – Modern Uses
> Talk about how surveyors use their equipment to set up right hand triangles in order to calculate distances etc…
> Have students using laptops research other possible modern uses for Pythagoras.
> If they cannot find any, have them brainstorm a list of possible fields that they think may use the Pythagorean Theorem.
Materials Needed:
o String and rulers
o White board, diagrams of tablet and Babylonian numbering system
o Laptops, paper to write ideas down on, pens
Post-Test: 3 min
Groups of three re-form and students teach other members about their area of expertise. Only have 1 minute each to share.
Summary: 2 min
Students complete the statement: The one thing I learned today that I didn’t know before was _______________________________________________________________.
(Orally if time allows.)
Group: Deb, Nadine, Michelle
Catch interest by having students form groups of three and numbering themselves 1,2,3 for jigsaw activity in which they will become the expert on some aspect of the history or modern use of the Pythagorean Theorem.
Learning Objective:
Students will be able to demonstrate an understanding of the Pythagorean Theorem by describing historical and contemporary applications of it.
> To learn a historical use for Pythagorean Theorem and to understand where Pythagoras' inspiration came from.
> To understand that this theorem came about from a practical application, not pen and paper theory.
Teaching Objective:
> Learn and improve our methods in conducting an engaging and educational lesson that will reach everyone.
> To interactively show the motivation for the Pythagoras Theorem, introduced to Pythagoras by the ancient Egyptians.
> To try out the Jigsaw strategy.
Pre-test: 1 min
> Who can tell me what we already know about the Pythagorean Theorem?
o Looking for formula, triples, and to see if anyone might already know where it comes from.
Participatory Learning: 7 min
> Split groups into 1’s, 2’s and 3’s.
o 1’s at Egyptian Station (Deb)
o 2’s at Babylonian Station (Michelle)
o 3’s at Modern Application Station (Nadine)
Station 1 – Egyptians
> Explain how ancient Egyptians used a right-triangle to redistribute fields after yearly flooding.
> Explain how they made a right triangle using rope and knots
> Explain how Pythagoras became involved/interested
> Make a right-triangle with a piece of string and ruler. Make a 3, 4, 5 triangle and see if they can find a right angle in the classroom with it.
Station 2 – Babylonians
> Explain Babylonian Mathematics and history of Pythagorean Theorem.
> Teaching Babylonian numbering system and ancient tablet.
> Briefly cover other ancient cultures in which Pythagorean Theorem was known and used
Station 3 – Modern Uses
> Talk about how surveyors use their equipment to set up right hand triangles in order to calculate distances etc…
> Have students using laptops research other possible modern uses for Pythagoras.
> If they cannot find any, have them brainstorm a list of possible fields that they think may use the Pythagorean Theorem.
Materials Needed:
o String and rulers
o White board, diagrams of tablet and Babylonian numbering system
o Laptops, paper to write ideas down on, pens
Post-Test: 3 min
Groups of three re-form and students teach other members about their area of expertise. Only have 1 minute each to share.
Summary: 2 min
Students complete the statement: The one thing I learned today that I didn’t know before was _______________________________________________________________.
(Orally if time allows.)
Group: Deb, Nadine, Michelle
Sunday, October 10, 2010
Mason, Thinking Mathematically. Ch 2&3 Response
The three phases of work are explained very thoroughly by Mason in Chapter 2 of his book Thinking Mathematically. I was struck by how detailed and structured each phase is. These three phases would be very beneficial for students in our classrooms to understand. I think that the entry phase would be particularly useful for students to further develop their skills. If the student does not plan out their attack first, then they will most likely to get stuck. However, if a student asks the three entry phase questions then they are most prepared to enter the attack phase. The first question (what do I know?) mostly involves organizing and categorizing data. This will greatly help students to know what data they have to use and also make sure that they use all the data. The second question (what do I want?) seems quite obvious but I feel is very often missed. Without fully understanding this vital point of the question, then the student spends unnecessary time working in the wrong direction. The last question (what can I introduce?) is great for students to realize this is where they can use their creativity and try different methods. Some areas to consider under this question are notation, organization and representation. After reading these two chapters I still believe that the entry phase would be the most important to spend time on with students. Too often this phase is rushed or skipped. I feel that this phase is the one that gives students most problems and causes them to get stuck.
Friday, October 8, 2010
Forbidden Territory
Mathematics is anything but unknown.
There are reasons, proofs, logic and solutions for it all.
Not only can answers be found, answers can be proven.
However, there is one little situation that renders unknown.
There is a black hole surrounding this dilemma.
It’s hard to believe because there are only two simple components.
The first component is divide and the second is zero.
Apart these two terms pose no issues or threat.
But if arranged one on top the other, this is forbidden territory.
There lacks a simple way to explain this phenomenon.
Inconsistency, irreversibility, indefinability and asymptotes.
Dividing by zero, one of the few things which math cannot do.
There are reasons, proofs, logic and solutions for it all.
Not only can answers be found, answers can be proven.
However, there is one little situation that renders unknown.
There is a black hole surrounding this dilemma.
It’s hard to believe because there are only two simple components.
The first component is divide and the second is zero.
Apart these two terms pose no issues or threat.
But if arranged one on top the other, this is forbidden territory.
There lacks a simple way to explain this phenomenon.
Inconsistency, irreversibility, indefinability and asymptotes.
Dividing by zero, one of the few things which math cannot do.
Wednesday, October 6, 2010
Timed Writing
DIVIDE
- Splitting and putting into smaller groups
- cutting something up unto smaller parts
- It could be a land into countries or a pie into slices
- a type of organization or grouping
- mathematically divinding- long division, fractions
- boundaries or lines
- smaller parts which all have something in common.
- smaller parts are different sizes or the same size
- sometimes division is not into nice whole numbers.
- dividing according to weight, value, size
- opposite of multiply
- faster than subtraction
ZERO
- nothing, none, zilch, absence, no items
- greater than -1 but smaller than 1
- in the middle of the negative numbers and positive numbers- divides the signs
- cannot divide by zero
- anything times zero is zero
- 0
- zero value, zero size, zero weight, zero time
- any value to zero? is it a value?
- integer
Simmt Article Response
There is a quote at the beginning of this article that I slightly disagree with. The quote states that "the study of mathematics is ultimately the study of humanity itself" (Devlin, 1988,9). I would change the quote to say that mathematics is the study of nature, and not humanity. I believe that mathematics is a man made construct to represent nature. Mathematics helps us understand the world in which we live in.
This article raised some valid points about mathematics education in schools contributing to citizenship. Mathematics develops reasoning, patterning, critical thinking and generalizing. I feel these qualities, without speaking in terms of mathematics, directly contribute to good citizenship education. These qualities also are heightened with the skill of explanation, which I think mathematics helps develop. Students practice communication in mathematics when they explain their though process to solve a problem. Another aspect of math that develops citizenship education is the view that there is not a single right answer, but rather multiple ways to solve one problem. This promotes the idea of diversity, different points of view and creativity.
This article raised some valid points about mathematics education in schools contributing to citizenship. Mathematics develops reasoning, patterning, critical thinking and generalizing. I feel these qualities, without speaking in terms of mathematics, directly contribute to good citizenship education. These qualities also are heightened with the skill of explanation, which I think mathematics helps develop. Students practice communication in mathematics when they explain their though process to solve a problem. Another aspect of math that develops citizenship education is the view that there is not a single right answer, but rather multiple ways to solve one problem. This promotes the idea of diversity, different points of view and creativity.
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