Weekly Report & Reflection Week #6!

Reflection 6- 

Witch's Recipe for Proportions

I can definitely say I enjoyed this week's class a lot as I learned a lot and got to do few challenging activities. I want my students to feel the same way when they are in my classroom. Each student in my classroom needs to feel that yes I am being challenged, but that challenge is at my level only. 

That takes us to differentiating instruction, which means to engage students in instruction and learning in the classroom. All students need sufficient time and a variety of problem-solving contexts to use concepts, procedures and strategies and to develop and consolidate their understanding. When I as a teacher would be aware of my students’ prior knowledge and experiences, I can consider the different ways that students learn without pre-defining their capacity for learning. So it comes all back to me as a teacher, I want to be the best math teacher out there. 

So, this week's class we learned mostly about proportions, what better way to learn about proportions than to engage students' in a witch's recipe? Yes, one of our activities was to mix a brew for the witches. I think that is a perfect way to engage students. They can have fun and be interested with the problem but also learn the core concepts. Concepts in the problems included multiplication, division, estimation, calculation, and proportions. 

Proportional thinking can be hard. It is not an easy concept for students to grasp. However, the different activities that we were shown in class by classmates was amazing and can be used for my practicum block that is coming up soon. That takes me to lesson planning. Today finally I had a practical experience with lesson planning. I had fun lesson planning and I think I was on track with it. I wasn't too sure about my lesson planning until the instructor showed us a video and explained step by step how one lesson plans. I have to thank that instructor for making it easier for us. 

After the video, I reviewed my lesson plan and thought I only need minor changes rather than major. That tells me that I am somewhat ready to lesson plan. Our instructor had divided our class into two and asked us to lesson plan in a large group. I got the witch's brew recipe problem and I got the perfect idea of how I would start my lesson if I were to teach that to my students. I would bring a large test tube with me and show them if I have 20 mL of water and I want to multiply it by number how would the amount of water change. 

That takes us back to the witch's problem because in that problem the recipe serves 3 people but we want it to serve 9, so we will have to multiply 3 by 3 to get nine. Hence, if water is an ingredient and we need to 20 mL for 3 servings, we can multiply 20 mL by 3 to get total of 9 servings. Therefore, this procedure applies to all the other ingredients on the list of a recipe. 

I think that assumptions and precisions matter when studying proportions!

Weekly Report & Reflection Week #5!

Reflection 5-

 The Mystery of Zero

The title of my reflection blog is 'Zero' today because that came up a lot in this week's session. What is the number zero? When you are a kid you learn that you cannot divide by the number zero. As we grow older we start to learn something different, we get the hint that if we divide by the number zero a lot of 'crazy' things happen. Today in class we were told that these things are against the laws of nature that we are so used to. So that's why we stay away from dividing by zero. 

But why?  Have you ever thought exactly why you cannot? I searched up to find some answers and I found this one by Dr. Tom:

"Because there's just no sensible way to define it.

For example, we could say that 1/0 = 5. But there's a rule in arithmetic that a(b/a) = b, and if 1/0 = 5, 0(1/0) = 0*5 = 0 doesn't work, so you could never use the rule. If you changed every rule to specifically say that it doesn't work for zero in the denominator, what's the point of making 1/0 = 5 in the first place? You can't use any rules on it.

But maybe you're thinking of saying that 1/0 = infinity. Well then, what's "infinity"? How does it work in all the other equations?

Does infinity - infinity = 0?
Does 1 + infinity = infinity?

If so, the associative rule doesn't work, since (a+b)+c = a+(b+c) will not always work:
1 + (infinity - infinity) = 1 + 0 = 1, but
(1 + infinity) - infinity = infinity - infinity = 0.

You can try to make up a good set of rules, but it always leads to nonsense, so to avoid all the trouble we just say that it doesn't make sense to divide by zero.

What happens if you add apples to oranges? It just doesn't make sense, so the easiest thing is just to say that it doesn't make sense, or, as a mathematician would say, "it is undefined."
Maybe that's the best way to look at it. When, in mathematics, you see a statement like "operation XYZ is undefined", you should translate it in your head to "operation XYZ doesn't make sense.""

You can find the above information and more from this website:
http://mathforum.org/dr.math/faq/faq.divideby0.html

You might also want to check this video out for more information:

That being said, let me briefly cover what we did today in class. We were introduced to the topics of integers and exponents. I learned that exponent is just a way to represent a given equation in order to shorten and simplify it. For example it is better to write 12^200 rather than to write 12 multiplying by itself 200 times. A lot more convenient.

In every class I learn something. This class I learned that sometimes to simplify math concepts you as a teacher have to 'lie'. For example, you have to say you can't divide by zero but in some dimensions of different mathematics you can. I also learned that we should watch out what we are saying as a teacher. For example it would be good to avoid saying "this is really easy" when in fact it is not easy. Not every student finds what you find easy is easy.

Weekly Report & Reflection Week #4!

Reflection 4

"Fractions, fractions, fractions!" Did we not hear that phrase when we were in elementary school? That was because we used to dread the topic. I am pretty convinced that is how students still feel about fractions if they have just starting the topic.

Not everyone feels comfortable with fractions, it can be a very complicated one because we are not working with whole numbers anymore. This is where I want to come in as a teacher candidate. I want my students to feel confident with their number sense skills whether it be a whole number or not. 

Phillip Martin. Phillip Martin Clip Art. Retrieved from
http://math.phillipmartin.info/home_fractions_01.htm

Today in class we focused on two topics: Fractions and Decimals. My three other classmates and I presented our activity learning task, a 10 minutes presentation plus 5 minutes for discussion. One person focused on decimals. He gave us out a really useful tool called the hundredths wheel. I think this is a tool I would definitely use with my students. 

Hundreths Wheel. Retrieved from
http://www.eworkshop.on.ca/edu/pdf/Mod27_representing_hundredths.pdf

Second really interesting method of calculating fractions is called the Macarena Method. I learned that from another presentation and it came to me as a complete surprise as I never heard of it before. I am convinced this method will help a lot of students, I do wish I knew that method myself when I was studying! If you want to check out the method see the video below:

I realized today in class that what math students really need is a tool and a platform. They need resources from which they can learn. The traditional way of teaching is no more and it does not teach anything. Students need to explore and discover. They need to make mistakes, fix and learn. This is math. The more variety of tools they have in their toolbox the more options they can have at problem solving. Just like how if a carpenter has more tools in his/her box he/she can do a lot more work than just one thing. 

Kids are capable to learn if they have, very much like the TEDx we saw in the TECH class. The speaker talks about how if you provide children with one computer and an access to internet they can teach themselves. I think that talk is worth to share it here too, please click HERE.

I think with that talk it would be a great place to end my post for the day. Stay tuned for next week's post. 

Learning Activity- Fractions

Learning Activity Summary

Topic: Fractions

Grade Level: 4

Mathematics Curriculum Strand: Number Sense and Numeracy Fractions

Content and Process Expectations: You can find in the Guide to Effective Instructions in Mathematics- Number Sense and Numeration Grades 4-6 Volume 5- Fractions. You can also find it in Chapter 11 of the course textbook ‘Making Math Meaningful.’

Source of Activity: www.eworkshop.on.ca

Approach

At a camp, campers stayed in 3 cabins. In cabin A there were 4 campers, in cabin B there were 5 campers and in cabin C, there were 8 campers. One day the campers were treated to pizza in the following way:

Cabin A- 3 pizzas, Cabin B- 4 pizzas, Cabin C- 7 pizzas

Pose the Question: Did some campers get more pizza than others, or did all the campers receive the same amount of pizza?
Clarify that:

·       all the pizzas are the same size;

·       the pizzas can be cut into any number of equal pieces.

Ask students to think about how they might solve the problem. Have students share their thoughts with a partner, and then invite a few students to share their ideas with the whole class. Provide an opportunity for students to ask questions about the problem or about possible approaches to finding a solution.

Pose questions that help students think about what they found out:

·       What strategy did you use to figure out the amount of pizza the campers in each cabin

·       How much pizza did each camper in each of the cabins receive?

·       Which campers received the most pizza? How do you know?

·       Which campers received the least pizza? How do you know?

Tools 

 You can use: Area model, fraction number lines or fraction bars

Assessment – things you need to check with the students

·       how well they understand the problem and whether they are applying an appropriate strategy;

·       whether they are dividing the pizzas into appropriate fractional parts (e.g., dividing a pizza into fourths for 4 campers);

·       how well they are relating division to fractions (e.g., 3 divided by 4 is 3/4);

·       how well they are comparing fractional parts (e.g. a fifth is larger than an eighth);

·       how well they are comparing fractions (three fourths is less than seven eighths).

Weekly Report & Reflection Week #3!

Reflection 3

Before class of week 3, I explored around the games that were posted by the instructor on SAKAI. There were three games: Prodigy, Canoe Penguins Race, and Demolition Division. I personally spent more time on the Canoe Penguins Race. It was a competitive game and I got to play with other people! We progressed in the canoe race by having the right answer to multiplication questions. I thought it was an amazing, interactive, and competitive game that can help you multiply in your head. It is definitely a good tool for learning multiplication. Students at grade 4-6 level will find it friendly competitive and interactive. Here are the links to the games:

Prodigy

Canoe Penguins Race

Demolition Division

            During class of week 3, my fellow classmates presented a mathematics learning activities. I got to see how you can teach one concept in many different ways. It was amazing to see the numerous models there are to teach one concept. I don’t remember being taught math that way. If I were taught math that way in my early years of school I would have understood it a lot better. It is good to know that there are many resources out there that can help us as future teachers to teach. These same resources and tools will hopefully help the students too.

            I think this class is not only about how to teach, but it is teaching me the math concepts itself too. I think it is great how I am learning the basics all over again because as I grew up the grades of educations, the basics were forgotten.  I think being a math teacher is a big responsibility. It is the case with any other subject too, but when learning math, students tend to stay away from it. Therefore, there is more responsibility now for a teacher to instill that motivation, inspiration and make the hard seem easy.

Dyslexia. Math Difficulties. Retrieved from
http://www.dyslexia.ie/information/information-for-parents/

            At the end of that class I have come up with 2 goals. One is that I want to learn more how to incorporate technology such as games into my teaching. More specifically, I want to be able to learn how to do that in my math classes. The second goal that I want to learn is how to model one concept in all the different ways out there. If I am able to model all the math concepts, then hopefully I can bridge the gap between the students and me, so that we can meet somewhere in the middle.

Clipart Panda. (2014). I Love Math. Retrieved from
 http://www.clipartpanda.com/categories/i-love-math-pictures