Skip to main content

Review of Class #10

Data Management and Probability


Data management and probability is in my opinion a critical strand of mathematics for students to learn. It is crucial because it helps to prepare our students for daily life by providing them with the necessary tools to collect, organize and analyze information that is all around them. Polls, trends and estimates are only a few examples of how data management is used in real life situations. Data management and probability can also be understood and recognized in various other subject areas such as social studied, health and physical education as well as science.

IFVP. Graphic Recording Data Management. Oct. 8, 2013. [Online Image]
Sourced from: http://bit.ly/2fKbYdG 

In order to insure that students have a strong conceptual understanding of data management and probability, it is important to tier instruction in a way that offers students opportunities to engage deeply with mathematical concepts and relationships. Teaching in tiers provides opportunities for instruction to meet the needs of students who are working at different levels of mathematical understanding. The following example of finding the probabilities associated with tossing two coins and the tiers at which the problem can be approached or extended is as follows: 

Tier 1: Students predict which outcomes: 2 heads, 2 tails, or 1 head and 1 tail, is more likely (or whether they are all likely) and conduct a probability experiment to test their predictions.

Tier 2: Students also consider the effect of the number of trials on experimental probability. They describe their reasoning in the context of typical misconceptions, such as "previous probability trials affect future trials" (for example, if a coin is tossed and comes up heads 5 times in a row, the probability of getting the head on the 6th toss decreases).

Tier 3: Students may also consider all possible outcomes (HH, HT, TH, TT) in order to explain why the probability of 1 head and 1 tail is 1/2, while the probability of 2 heads is 1/4. This is a first, informal step towards the development of an understanding of theoretical probability.
      
It is important to offer various meaningful and engaging learning activities that are tiered to foster a deeper understanding of data management and probability. Activities should center around; collection and organization of data, data relationships as well as probability. Teachers can facilitate this understanding by designing activities where students; collect and organize primary and secondary data, interpret and use charts and graph, including continuous line graphs, explain relationships between data sets and draw inferences from data, and determine the theoretical probability of an outcome in a probability experiment.

From stock markets to polls, to election predictions and results, data management is all around us. As educators it is our job to open the eyes of our students so that they recognize the significance that data management and probability has in our everyday lives.

Cheers until next week!

Ashley 

References:

Ontario Ministry of Education. Data Management and Probability, Grades 4-6. 2008 [Online Document]. Sourced from: http://eworkshop.on.ca/edu/resources/guides/Guide_Data_Management_Probability_456.pdf


Comments

Post a Comment

Popular posts from this blog

Rich Tasks for Week Four

This week in math we discussed the importance of providing students with rich tasks rooted in mathematics. A rich task encourages students to think creatively, work logically, communicate ideas, synthesize their results, analyze different viewpoints, look for commonalities and evaluate findings. San Jose Library. Group Work on Cards. July.1,2009. Retrieved from: http://bit.ly/2woSSlZ  For a task to be rich it must be engaging in the sense that it has the potential to engage students in mathematical thinking. It must also have a meaningful mathematical focus that connects to the mathematics curriculum, process and content expectations.  It is important to challenge students meaningfully through problem solving. A rich task will be grounded in problem solving and will encourage students to reason his/her way to new understanding. The student would accomplish this by using multiple math processes while the instructor would allow ample time for explanation, justi...
4 comments
Read more

Growth Mindset for Week Two

This week in mathematics I have learned and applied my newfound growth mindset. I countered my fixed way of thinking with positivism, telling myself that if I apply myself and use my conceptual knowledge, I too can prevail in math. City Year New York. Growth Mindset. Feb.16,2016. Sourced from: http://bit.ly/2ffB0GL  When the professor attempted to explain the card trick in a mathematical formula, my mind reverted to a fixed way of thinking. My initial reaction was that I couldn't do it and I began to "check out" of the demonstration so to speak. Being a reflective practitioner and student, I realized that I needed to have more confidence in myself and my abilities. I will honestly say that it took some time for me to understand how the formula was rewritten (ie. algebraically). I did eventually come to an understanding and I think that it is evidence that my mindset is changing. As educators we must model attitudes and behaviors for our students. If we model a ...
Post a Comment
Read more

Learning Styles in the Classroom for Week Three

This week in mathematics we focused on the gratification of mathematics as well as understanding how to approach various types of learners in the classroom. JoanDragonfly. Venn Diagram of 3 Learning Styles. June.8,2017. Retrieved from: http://bit.ly/2y2gQrz  I had fun trying various tests that helped me to identify what type of learner that I am and surprisingly I have discovered that I am equally an audio and visual learner. I think it is imperative that instructors design their lessons, delivery, and classroom environment to enrich and engage various types of learners (ie. kinesthetic, visual, and audio).  I think it is important that we encourage students to understand how they learn best whether it be auditorally, visually, or kinestheically. With this being said, I also think that educators shouldn't encourage students to label themselves. When someone labels themselves as a certain type of learner, I believe that students may internalize that definition ...
1 comment
Read more