Hi everyone,
Here Ying Ting's EDCP 342 Unit Plan for my Grade 11 class.
P.S. Susan, I have already emailed you the PDF separately. I'm posting on the Blogger so it would be easier for you to comment directly on here.
Enjoy!
Monday 25 January 2016
Friday 4 December 2015
Response to John Mason's Article: Questioning in Math Education
1. Do Mason's ideas might connect with inquiry-based learning in secondary school mathematics? (Why or why not?)
From reading through the article, I do think that Mason's ideas on math teaching can connect with inquiry-based learning in secondary school mathematics. Because high schools can be quite challenging and even competitive for some students as they are wanting to get through each grade and to be able to graduate on time, students can often feel pressured into knowing everything that's being asked, or feel overwhelmed with the expectations from their math teachers. With Mason's teaching strategies, teachers are not seen as an authoritative figure that's standing in front of the classroom. Rather, they are seen as someone who really value the opinions and questions of students, who care for student learning, and who respect students without having them to feel excluded of being incapable to think beyond their abilities or doubt. These forms of math teaching allow students to think and inquire for themselves while actively collaborating with their teachers and classmates.
2. How might Mason's ideas about questions in math class be incorporated into your unit planning for your long practicum?
Mason's ideas about questions in math class can be incorporated into my unit planning through giving students more time to ask questions continuously through the lesson. If I give a word problem during my lesson that students can work on to reinforce the content, I can ask students to work on their own first, then pool their answers together regardless if they are right or wrong, instead of telling them the answer right away or instead of telling them that these are wrong answers. I can then work through the problem step by step, so students can keep track of what they did and compare it with my solution (as if I were also a student). I can also ask the students to come up to the board and ask them to solve it step by step. Even if we made a mistake, we will know that it's okay and so we try again to find the right answer, to become "stuck then unstuck" (Mason) allows students to see that there are possibilities to get to the right answer from where they are.
From reading through the article, I do think that Mason's ideas on math teaching can connect with inquiry-based learning in secondary school mathematics. Because high schools can be quite challenging and even competitive for some students as they are wanting to get through each grade and to be able to graduate on time, students can often feel pressured into knowing everything that's being asked, or feel overwhelmed with the expectations from their math teachers. With Mason's teaching strategies, teachers are not seen as an authoritative figure that's standing in front of the classroom. Rather, they are seen as someone who really value the opinions and questions of students, who care for student learning, and who respect students without having them to feel excluded of being incapable to think beyond their abilities or doubt. These forms of math teaching allow students to think and inquire for themselves while actively collaborating with their teachers and classmates.
2. How might Mason's ideas about questions in math class be incorporated into your unit planning for your long practicum?
Mason's ideas about questions in math class can be incorporated into my unit planning through giving students more time to ask questions continuously through the lesson. If I give a word problem during my lesson that students can work on to reinforce the content, I can ask students to work on their own first, then pool their answers together regardless if they are right or wrong, instead of telling them the answer right away or instead of telling them that these are wrong answers. I can then work through the problem step by step, so students can keep track of what they did and compare it with my solution (as if I were also a student). I can also ask the students to come up to the board and ask them to solve it step by step. Even if we made a mistake, we will know that it's okay and so we try again to find the right answer, to become "stuck then unstuck" (Mason) allows students to see that there are possibilities to get to the right answer from where they are.
Thursday 3 December 2015
Reflection on Dave Hewitt's Video
Our class watched two parts of the video that focuses on Mr. Hewitt's teaching strategies on mathematics for elementary and middle school children. The video was very inspiring as it allowed me to think of some the practical teaching methods that I could incorporate into my classrooms. From the video, I really admired the various scaffolding techniques that Mr. Hewitt used in bringing movement, sound, wait time, repetition, and discussions into his teaching method. I could see that students were more engaged from implementing this strategy. I also noticed that Mr. Hewitt didn't speak much or jump in right away when asked a question, but rather he let students to think through the problem and work out themselves, little by little, until they get the right answer. Even though his presence and authority is still in the room, it seemed as if he gained students' respect and trust in creating a more comfortable environment for students' learning, regardless if they made a mistake or not. I had learned a lot from Mr. Hewitt's teaching strategies, and I need to keep them in mind when I teach math classes in the future!
Tuesday 1 December 2015
Reflection on Micro-teaching 2
For our second micro-teaching this Monday, Etienne, Deeya and I were presenting our lesson on the Sine Law. I reflect that our teaching topic was interesting, and the materials were a definite bonus to help students visualize. However, the lesson was a bit rushed. I think the reason is that we had three people in the team, with each presents a different sub-topic of the Sine Law, there were a lot of information that we would like to cover for each case. Having 3-4 students per team and let them learn in less than 3 minutes might not have been enough before rotating them and starting on a new sub-lesson. I found that our discussions were cut short due to lack of time, even though there were still a few more ideas to discuss. Furthermore, we should have had a more well-rounded closing/conclusion before ending the lesson.
Sunday 29 November 2015
Micro-teaching 2: Lesson Plan for Sine Law
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Title:
Learning the different cases of the
Sine Law
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Date:
November 30, 2015
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Grade
Level:
Pre-calculus 11
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Prescribed
Learning outcomes:
·
Be able to
understand how to apply Sine Law to solve problems.
·
Introduce
oneself of 3 different cases of triangles in applying the Sine Law.
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General
purpose:
The class will look at how the Sine
Law can be used to find the unknown length of the side of a triangle given
one angle and the length of the other two sides.
We will look at three (3) cases:
1.
Where there is
no solution,
2.
Where there is
one solution,
3.
Where there are
two solutions.
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SWBAT
3.5
Sketch a
diagram and solve a problem, using the Sine Law.
3.6
Describe and
explain situation in which a problem may have no solution, one solution, or two
solutions.
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Probing
of Previous Knowledge
·
The class has
already been introduced with the notion of Sine Law (the relationships
between the sides and angles) and the proof of Sine Law.
·
The class understands
basic properties of triangles and knows how to draw a triangle, such as labelling
the angles, sides, and the height, respectively.
·
The class understands
the concept of SOH-CAH-TOA; students are expected to know how to calculate
the height of a triangle using SOH-CAH-TOA.
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Objective
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Time
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Activity
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Materials
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Introduction
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1 minute
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·
Ask students
where they see the use of trigonometry in their everyday life.
·
Provide more
background info on trigonometry that appeal to them.
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Summary
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2
minutes
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·
Ask students if
they can recall what sine law is (just in case not everyone does).
·
Draw a generic,
3-sided triangle.
·
Review the
concept of Sine Law.
·
(With a diagram)
Ask students if they can find an unknown angle or length of a triangle given
the other two lengths and an angle.
Is this always
possible?
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Whiteboard
Markers
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Inquiry
Project
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10
minutes
The instructor will spend 3 minutes
with each group, then rotate for a total of 9-10 minutes.
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·
Introduce to
class the three (3) different cases of the Sine Law.
·
Divide the class
into three groups.
Within each group:
·
The instructor presents
a different case.
·
The instructor
gives each student a set of 3-4 sticks, where students have to make as many
different triangles as they can think of.
·
Once students
are finished making their answers, they have to explain their answers to the group.
·
The instructor
will help to guide the students, writing the problem on the board and
explaining why there is indeed only one, two, or no solution.
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Measured sticks with which to make
triangles.
Multiple sets for each of the three
cases.
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Handout
+ Summary
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3 minutes
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·
Provide the
class with handout on the three cases of Sine Law.
·
Go over the
handout briefly.
·
Use it to show
students that the three different cases necessarily have one, two, or no
solutions.
·
Illustrate this
on the whiteboard.
·
Show the
implications of this when solving the Sine Law.
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Students may need pen and paper for
this.
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Summary
Evaluation:
By having the students learn from
doing hands-on activities with the sticks (and other visual tools), they can
understand better the numbers of triangles that can be made given certain
angles and lengths.
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Thursday 26 November 2015
Sunday 22 November 2015
What is arbitrary and necessary in teaching (math)?
1. What does Hewitt mean by "arbitrary" and "necessary"? How do you decide, for a particular lesson, what is arbitrary and what is necessary?
According to Dave Hewitt, in a learning setting, "arbitrary" means that students are informed of the learning materials through external sources, such as teachers, books, the internet, and many others; "necessary" means that students do not need to be informed of the learning materials through external sources. Often times, they can work through the questions and figure out themselves. As Hewitt writes in his article, what is "arbitrary" is in the "realm of memory", and what is "necessary" is in the "realm of awareness". I have encountered this kind of thinking and reasoning during my short practicum. There were times when students asked why it must be this way and not that, in which I hear my teacher say, "Sometimes, things are just easier this way." I think many of us new and experienced teachers have asked ourselves this kind of question many times during our teaching, and many of these examples have been cleverly brought up by Hewitt.
For my teaching, personally, I would consider math symbols, notations, or any naming conventions as something that is arbitrary. I am unsure of how I can explain why 2 is bigger than 1, for instance. Number symbols (e.g. 1, 2, 3,...) are universal across the world, so explaining that to students would be difficult for me because we have been taught and memorized this way since the beginning.
I would consider proofs, properties and relationships to be necessary because in many of these cases, they can be derived and worked out by students; students within "awareness" that is. For example, understanding why a parabola is shaped a certain way can be understood by graphing and interpreting the formula because parabolic formulas can be revised. Similarly, one can probably also work out why Speed = distance / time, or why chemical formula is written this way because these formulas can be derived and solved from real-life applications, whereas symbols and notations do not.
2. How might this idea influence how you plan for your lessons, and particularly, how you decide "Who does the math" in your math class?
Hewitt's idea of what is arbitrary and what is necessary really blows my mind on thinking to myself and asking "why". There might even be questions that some university professors and teachers cannot answer because they themselves learned concepts arbitrarily. As a teacher, I will try to dig deeper on the materials being taught in class for the curious minds. I might explain, on the side, why we do math a certain way while showing and explaining that there are alternative methods to do math differently, but it would just be harder for some students to grasp (although they are not limited to solving math their own way as long as they derive a right answer in the end). I know that not all students are capable of understanding the "necessary" component to math, but as long as teachers have an answer to "why", they can use simple hints so students can really ponder on it and "think about it".
According to Dave Hewitt, in a learning setting, "arbitrary" means that students are informed of the learning materials through external sources, such as teachers, books, the internet, and many others; "necessary" means that students do not need to be informed of the learning materials through external sources. Often times, they can work through the questions and figure out themselves. As Hewitt writes in his article, what is "arbitrary" is in the "realm of memory", and what is "necessary" is in the "realm of awareness". I have encountered this kind of thinking and reasoning during my short practicum. There were times when students asked why it must be this way and not that, in which I hear my teacher say, "Sometimes, things are just easier this way." I think many of us new and experienced teachers have asked ourselves this kind of question many times during our teaching, and many of these examples have been cleverly brought up by Hewitt.
For my teaching, personally, I would consider math symbols, notations, or any naming conventions as something that is arbitrary. I am unsure of how I can explain why 2 is bigger than 1, for instance. Number symbols (e.g. 1, 2, 3,...) are universal across the world, so explaining that to students would be difficult for me because we have been taught and memorized this way since the beginning.
I would consider proofs, properties and relationships to be necessary because in many of these cases, they can be derived and worked out by students; students within "awareness" that is. For example, understanding why a parabola is shaped a certain way can be understood by graphing and interpreting the formula because parabolic formulas can be revised. Similarly, one can probably also work out why Speed = distance / time, or why chemical formula is written this way because these formulas can be derived and solved from real-life applications, whereas symbols and notations do not.
2. How might this idea influence how you plan for your lessons, and particularly, how you decide "Who does the math" in your math class?
Hewitt's idea of what is arbitrary and what is necessary really blows my mind on thinking to myself and asking "why". There might even be questions that some university professors and teachers cannot answer because they themselves learned concepts arbitrarily. As a teacher, I will try to dig deeper on the materials being taught in class for the curious minds. I might explain, on the side, why we do math a certain way while showing and explaining that there are alternative methods to do math differently, but it would just be harder for some students to grasp (although they are not limited to solving math their own way as long as they derive a right answer in the end). I know that not all students are capable of understanding the "necessary" component to math, but as long as teachers have an answer to "why", they can use simple hints so students can really ponder on it and "think about it".
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