Blog Post 6: EDBE 8P29 (October 21st, 2016)

Good Day Bloggers!

Objective: 

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P29 at Brock University! To begin this class, we reviewed Number Sense And Numeration, and specifically Ratio, Rates and Proportions as outlined in the Ontario Math Curriculum Grades 1-8. 

Teagan and the Friendly Giant: 

The problem represented to the class was Teagan and the Friendly Giant. Teagan measured herself and was 6 of her little hands tall. The friendly giant measured himself and he was 6 of his big hands tall. He measure Teagan and she was 4 of his hands tall. How many little hands tall is the friendly giant?

We solved this problem in groups of three using problem solving and communication skills. I thought this was a great exercise, as students even in our teachers college course were at first coming up with different answers, but we collaborated with one another to find the correct answer.

Presentations:

We next began our presentations, where 3 Teacher's College Candidates have 10 minutes to present their presentations on the session topic.

Ratio, Rate, and Proportions:

Today we discusses the differences between ratio, rate and proportions. Ratio: a comparison of quantities with the same units. It can be expressed in ratio for (3:4) or as a fraction 3/4. Rate: A comparison, or type of ratio, of which two measurements with different units such as distance and time (100km/hr). Proportion: An equation showing equivalent ratios in fraction form; 2/3= 6/9. These expectations are found in the Number Sense and Numeracy section under Proportional Relationships.

It is important for students to have a good conceptual understanding of fractions and ratios before attempting to solve proportion problems.

                                                               Rates/Ratio/Proportions

Misconceptions: 

It is also important to be aware of possible student misconceptions. It is not enough to just tell the student that their misconception is wrong, rather as educators we must identify students' misconceptions, Provide a way for students to confront their misconceptions, and help students reconstruct and internalize their knowledge, based on correct conceptions. An example of a student misconception is that they believe the world is flat. This is most likely a preconceived notion, and it is our job to understand the differences between various misconceptions and that there are different ways of correcting this misconception, even with as simple as changing one key word in what you are describing can make a world of difference. 

Reflect: 

In this session, we discussed problem solving and communication strategies, the difference between ratio, rate and proportions, and learning about students misconceptions. We discussed the different misconceptions, and how some misconceptions can be easily addressed by simply using a different word to describe the problem, but that some student misconceptions are much more deep and thus takes time and commitment to address these misconceptions. For ratio, rate and proportion, we can 

ensure students develop a conceptual understanding with manipulatives, examples, reflection, etc. to allow students to absorb these three differences and have a distinct understanding of what is being instructed to them.

Blog Post 5: EDBE 8P29 (October 14th, 2016)

Good Day Bloggers!

Objective: 

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P29 at Brock University! To begin this class, we reviewed our problem solving assignments, and the issue that most people had were to compare their problem solving activities to specific curriculum expectations outlined in the Ontario Math Curriculum Grades 1-8. 

                                                     Battleship in Mathematics Anyone?

žJeopardy Battleship:  

Following the review of the previous week as well as our assignments we were handed back, we played Jeopardy Battleship! The purpose of this game is to be the last person standing, relying on your math skills and some luck. First, we were instructed to shade in the squares representing each type of ship (three ships), and also to draw a missile on one of the squares. If it lands on your missile than you get to pick the next square. Once all your ships are sunk then you join another player’s team.

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While I thought this game to be engaging, for younger students this could be a really confusing concept, so as a more fast paced game to begin with, it might be more efficient to learning to slow down the battleship sinking so students having difficulties with mental arithmetic can be inclusive to the game as well.

Presentations: 

After the Jeopardy Battleship game, we had 3 presentations of 10 minutes in length performed by various students in the class. I like this aspect of the course because it allows us to perform a mini lesson and can get feedback both from our peers and the teacher to perfect our presentation image for the time that we engage young students in our practicum.

Number Sense and Numeration Expectations: 

Grade 4: Solve problems with +, -, x, / of single digit and multi-digit whole numbers, + and - decimal numbers to tenths and money amounts

Grade 5: Solve problems with x, / at multi-digit while numbers, + and - of decimal numbers to hundredths

Grade 6: Solve problems with x, / of whole numbers, + and - of decimal numbers to thousandths.

Grade 7: + and - fractions, solve problems with whole numbers and decimal numbers

Grade 8: Solve problems with whole numbers, decimals, fractions and integers (including x and / of fractions) 

Integers and Exponents 

Next, we discussed integers and exponents, and how we can use real life situations to explain to young students how they already use integers and exponents without even realizing it through money problems, temperature, etc. Using coloured tiles for adding and subtracting integers also is beneficial to students, because you can allow students to have a visually appealing and interesting way of showing that the problem 5/2 is not 5 x 2, rather it is 5 x 5. 

When? 

Lastly, we discusses the question of when. When should teachers introduce a new concept to aid in discovery or to help them go from a concrete idea to an abstract idea? In what cases should teachers need to re-teach a topic or to develop the understanding of a concept? These are very important questions that I will have to ask myself when I am provided the opportunity to teach a classroom of students, and I will have to aim to their individual needs to determine an answer for these questions. 

Reflect

In this past session, we reviewed mental arithmetic and number sense and numeration. We discussed in detail about integers and exponents, and the use of manipulatives. Some strategies can you use to make sure your students do not become dependent on manipulatives are to have the student preform the equation/question in multiple ways; with and without the manipulatives, to ensure the students complete understanding of what is being taught. Specific to how to ensure students development and conceptual understanding of integers and exponents, I would use various manipulatives such as blocks, or anything the student could visually count with, and allow them to see that 5 / 2 is different then 5 x 5. What could also work is allow the students to draw out the problem themselves and then to group 5 sets of 5 to 5 times 2 and compare the differences!

That's all for now! Until next time bloggers!

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Blog Post 4: EDBE 8P29 (October 7th, 2016)

Good Day Bloggers!

Objective: 

For this week, it is my objective for this blog post to present my responses to questions, ideas and information presented this week in the course EDBE 8P29 at Brock University!

Class Activities (Teachers in Training): 

This week in class, we began with an online dice game, used as a method for young students to learn about place value. The general gist of this game were to draw four boxes on a piece of paper, with the digits aiming to as close to ONE as possible. For example: 0.4567 or 0.5476 (which number is close to one?) We were taught that this game could be very motivating and encouraging for students, as it was fun four our class. I found this to be a great introduction to the class, as it got the class attentive and eager to learn about how to teach the order of decimals. Next, we learned about understanding about the function of the denominator. We used images like pizza and cake slices, and we were taught that we could use blocks in order to teach fractions.

                                                         Manipulatives For Place Value




After this, we began with the three presentations of the week.

Following this, reviewed number sense and numeration. We reviewed the grade 4 and 5 standards as an example: in grade four, students are expected to count forwards and backwards by (0.1 and fractional amounts up to 1/10) and in grade five (1/100). We next discussed a grade six lesson. Following this, and to conclude the class, we were engaging ourselves in a Tarsia puzzle, which I personally had a great time doing because it was challenging. It was a great way to practice mental math with fractions, as the purpose of this game for students is to challenge their fraction sense at a fast pace.

Reflection: 

I thoroughly enjoyed this lesson, as it challenged us as teacher candidates and the lessons we learned about how to teach students. I could definitely see myself in the future using the Dice and Tarsia games in my own classroom should I have the opportunity to teach elementary level mathematics.