Reflection - "Hypothetically: 10 Years on..." Blog Post

This exercise made me realise that no matter how hard I work at being a great teacher there will always be students who do not like my methods or even me personally. I will have to ensure that when this happens I do my best for the student but do not take it to heart. Thinking back on my old math teachers I realise that after many years I still remember them and my students will still remember me. So much happens during high school years that I took for granted that as a teacher I will not only affect my students during those years but for many more to come, they will remember me just as I continue to remember my teachers. There will be highs and lows during my teaching career, and although it is intimidating thinking that I will be affecting the lives of so many students, I believe it will be an incredibly rewarding career.

Group Micro Teaching – Apprenticeship and Workplace 10

Michelle, Deb, Nadine

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.

Ø  To learn a historical use for Pythagorean Theorem and to understand where Pythagoras' inspiration came from.

Ø  To understand that this theorem came about from a practical application, not pen and paper theory.

Teaching Objective:

Ø  Learn and improve our methods in conducting an engaging and educational lesson that will reach everyone.

Ø  To interactively show the motivation for the Pythagoras Theorem, introduced to Pythagoras by the ancient Egyptians.

Ø  To try out the Jigsaw strategy.

Pre-test: 1 min

Ø  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

Ø  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

Ø  Explain how ancient Egyptians used a right-triangle to redistribute fields after yearly flooding.

Ø  Explain how they made a right triangle using rope and knots

Ø  Explain how Pythagoras became involved/interested

Ø  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

Ø  Explain Babylonian Mathematics and history of Pythagorean Theorem.

Ø  Teaching Babylonian numbering system and ancient tablet.

Ø  Briefly cover other ancient cultures in which Pythagorean Theorem was known and used

Station 3 – Modern Uses

Ø  Talk about how surveyors use their equipment to set up right hand triangles in order to calculate distances etc…

Ø  Have students using laptops research other possible modern uses for Pythagoras.

Ø  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.)

Reflection - "Thinking Mathematically" Chapters 2 & 3

I love that this book does not presume we are all able to do all the problems and does not make us feel bad when we can't. Everyone is different and different people struggle with different problems regardless of their ability. If you don't at first appreciate the simplicity of the language I'm sure you will at some point come across a problem which stumps you at first and makes you realise how valuable and confidence inspiring this is.

I will definitely use the "how much dirt is there in the hole" problem. I think this would be very good for proving to students it is vital to READ the question! Extending problems is also something I wish to bring to the classroom, I want my students to be creative and extend problems they have worked on and I believe they should get marks for doing so. This will not only get them thinking further but will solidify in their minds what they have learnt from the original problem.

"What do you know? What do you want? What can you introduce?" is something that I frequently tell students to ask themselves when problem solving. Students tend to look at a problem and if they don't immediately know the answer or have seen a parallel problem solved get disheartened and find it difficult to continue.  Breaking down the problem solving process into manageable steps is invaluable and often overlooked by students.

These chapters reinforce that it is OK to get stuck and that once there there are logical steps you can take, there is still progress that can be made.

3, 2, 1, DIVIDE!!!

To divide or not to divide
That is the question
Dividing can give us less
or it can give us more
It can also give us a headache
Especially if zero is involved

Zero, the angelic numerator
The devilish denominator
Zero is interesting
Zero is infuriating
Zero, a number or not a number
That is the question

Reflection on Article - "Citizenship Education in the Context of School Mathematics"

I loved the opening of this article, that "mathematics education is crucial in the development of informed, active and critical citizens" and I strongly agree. So much in society is quantified and without a strong understanding of mathematics citizens will not fully understand their society. For instance, the government uses a lot of statistics to explain their ideas but without a mathematical education one may not question the data that was used to produce these statistics. If unable to ask such questions one is a mere spectator rather than a participator in the world.


I also agree with the point the article makes regarding making students active participators. If they are more involved in the classroom they are more equipped to be involved in society.  I believe it is our responsibility as teachers to create a flexible learning environment in which there is room for the students to express their creativity, to not only solve problems but to create them too. However I do draw the line at having the students judge the adequacy of their and their peers solutions. Of course their opinions should be heard but at this learning stage I feel it is important to always get feedback from the teacher, after all, if the students are posing the problems, solving them and assessing each other, what need is there for a teacher?

Timed Writing Exercise

Divide:

Divide to me firstly is a mathematical operation, although it has many other uses in the English language. I believe divide often has negative connotations, people who are divided over an idea may argue, wars happen due to division. Divisions in society often is a cause for tension. Divide and conquer is often heard, thus implying division  creates weakness. Divide can also be positive, someone may divide their lunch with their friend, thus sharing.

Zero:

Nothing, empty. Cannot be a divisor - relation to word above. If the remainder is zero the numbers (or polynomials) divide perfectly. Zero brings to mind more mathematical ideas than ideas in the English language. Countdown, when zero is reached we have blastoff!