Week 10: Report and Reflection

This week our class focused on Data Management & Probability. Data Management & Probability is a large topic to cover because there are ways in which we collect and describe data, ways that we display and analyze our data, and also how do we measure the likelihood of the next event based on our data.

I thought that Jeff's activity was an appropriate way to get students engaged with the ways in which we collect and organize data through the mean, median and mode. After going through some modelling he asked use within our groups to find the mean, median, mode and range with our collection of shoe sizes. He also presented the question in the context of a real-life situation. We were to imagine we were a shoe company and by calculating the the mean, median and mode of our data we were able to see why a company would want to know this information, because it helps to better plan with manufacturing. Activities like this allow for students to connect reasons where we use mathematics in real-life and also why we use mathematics.

Asma's activity clearly identified the uses of bar graphs and how to represent data. What I find to be most effective in teaching how to represent data is the use of asking students questions that pertain to their interests. Asking them about favourite colours, or shoe sizes allows them to record what they are familiar with in order to simplify the concept. I also enjoyed the activity itself which allowed students to work with a partner to record the rolls of their dice. This presented a way of collecting random data and also made the activity feel like playing a game.

Asma's Activity
Chamberlain, 2015 (C)

People Graph
Small, Marian. Making Math Meaningful. p.520

Representational Graph
Small, Marian. Making Math Meaningful. p.521

Making Math Meaningful also identified various ways of representing and communicating data. I think having students create concrete graphs, people graphs or with representational objects, are an effective way for having students visualize the concept of graphing more thoroughly. People graphs suit the contexts where students are graphing personal data, such as choices or opinions. (p. 520) Representational graphs use objects or manipulatives. Asking students to create people graphs will help students communicate graphic visually and also orally because the whole group could create a discussion based on how they have graphed themselves. Representational graphs using objects would allow for visual comparisons and also connecting with real life objects. I feel that using concrete methods of graphing would be a necessary step to take prior to having students record actual graphs on chart paper because they would have a better sense of the purpose of graphing.







Resources:
Small, Marian. Making Math Meaningful to Canadian Students, K-8. 2nd Edition. Nelson: Toronto, 2013.

Week 9: Report and Reflection

What I am enjoying most about the readings from the text book is that it allows us to distinctly define the topics of study. For instance the book explains measurement and that "it is about assigning a numerical value to an attribute of an object, relative to another object called a unit. Usually, you measure to have a sense of the size of an object compared to other objects whose size you know. A greater measurement implies that one object has 'more' of a particular attribute than another." (p. 412) I find that it is helpful, as a teacher candidate unfamiliar with mathematics, that it is extremely useful to be able to define topics in this way. It helps for a better understanding when revisiting the methods and work involved in that topic.

I also learned about addressing Measurement Principles in the classroom (p.413):

• Different measurement attributes of the same object are not always related, so it is possible for an object to be large in one way and to be small in another
• Sometimes you measure directly and sometimes you measure indirectly
• Most measurements can be determined in more than one way
• Familiarity with certain measurement referents helps you estimate
• There is more than  one possible unit that could be used to measure an item, but the unit chosen should make sense for the object.
• In order to measure, a series of uniform units must be used, or a single unit must be used repeatedly

Lory Evans 2nd Grade Page. URL: http://bit.ly/1NyG7FL

In going over these principles, I can see the importance of all of these would be in teaching measurement and would have to be carefully considered while constructing a unit on measurement.
Reflecting on the class presentations, I was able to see how our presenters were able to construct various measurement principles within their chosen activity.

I can envision using Tim's activity of asking students to come up and measure their height. Not only is this engaging and as a fourth grade student probably very exciting to come up and be measured in front of the class. But this activity also inadvertently instills various measurement principles within it.  This activity presented the principle that "sometimes you measure directly and sometimes you measure indirectly". We were asked to estimate the heights of our teacher candidates after having our heights marked on the board, this would be indirect measurement because we are guessing based on what we know about measurement in real life. There is also the principle tied into this that "most measurements can be determined in more than one way," and also "familiarity with certain measurement referents helps you estimate." For example, Dylan pictured the height of a meter stick and envisioned it's length to compare what the heights may be. For myself, I knew my height in feet and inches (imperial system) and I used my height to compare to what the other heights may be. Once I started with the imperial system I had to change this to metric, and I did not know how to do this using Tim's chart, but what I did know is that there are 12 inches in every foot, and about 2.5 cm in every inch. I am 5 ' 2", so I converted my feet into inches, 5 feet x 12 inches = 60 + 2 extra inches = 62 inches. And if one inch equals 2.5 cm, than 62 inches x 2.5 cm = 155 cm. Using this strategy I was able to estimate the heights effectively which were only very few centimetres off from the actual heights. It is interesting the different methods students will use to make their estimates.

Anthony's activity presented area and perimeter and what I would like to make note of from this are the various ways students were able to calculate area of misshaped figures. Different students came up with ways they would split the figure, and some students would calculate the whole area and use subtraction to take away the areas that did not exist in the shape. Again, it is interesting to encounter to various ways students will approach problem solving and what they can envision in their heads.

Chamberlain, 2015 (C)

What interests me about the chapter that did not really come up in the activities is qualitative measurement - although Tim did describe the distinction between qualitative and quantitative measurement - I am curious about this topic because it presents how we can measure without using rulers. We can measure with other tools, almost anything we can find, in order to get an approximate measurement. Below is an image from page 436 of the text book, which uses pennies to calculate area. For students just learning area this would be a great way to explain the concept of area, being that it is the measurement that fills the entire inside of a shape. This is also effective because it builds a schema of measurement for students, if they are in a real world situation where they may need to estimate, they can figure out that a penny is almost 2cm wide, and would be able to envision pennies or physically line pennies up to come up with a measurement.

Small, Marian. Making Math Meaningful. p.436

Resources:
Small, Marian. Making Math Meaningful to Canadian Students, K-8. 2nd Edition. Nelson: Toronto, 2013.