We Need More Portfolios in Math Class!

Welcome back! Thanks for sticking it out with me. It's been a wild semester and we're almost at the end. Just two weeks to go. This week in class we discussed the difference between assessment and evaluation and the assessment cycle that often takes place in the math classroom.

Let's start with the difference between assessment and evaluation. As teachers, when we assess, we are looking at what students are doing and how they are doing it so that we know how to adapt our instruction based on our students' needs and interests. When we evaluate, we are assigning a grade level to work completed by the students to help us when reporting back to parents on their child's progress.

(2017, November 24). Image provided in class.

 The assessment cycle presented in class, the one you can see on the right, explains how expectations drive the tasks given to the students, which drive the assessments, which drive the expectations. Within this cycle, we have the triad of Observation-Conversation-Product, which we have learned about in our other classes. This triad of information supports teachers when it comes time to evaluate students. It provides teachers with a more holistic and accurate understanding of the student's knowledge, so I find it very fitting to be included in this assessment cycle.

Now that we have those little pieces of information, let's get down to what I really want to talk about: portfolio assessment.

As described by Learn Alberta, a portfolio is a purposeful collection of student work samples, student self-assessments and goal statements that reflect student progress. In mathematics, portfolios are excellent assessment tools because they allow students to see their academic progress and mathematics is a very progressive subject. That means, that what one learns early on establishes the foundation on which students will build their future math knowledge. They are constantly reviewing skills and learning new ones to develop the previously mastered skills, and a portfolio shows proof of that.

Portfolios allow teachers to conduct a specific type of assessment that we learned about this week; that is, assessment as learning. Assessment as learning allows students to monitor their own learning and get feedback to make changes and adjustments in what they understand.  This type of assessment allows students to reflect more deeply on their strengths and weaknesses in mathematics and thus, allowing students to be in charge of their own learning.

When students are in charge of their own learning, they become more resilient in persevering through challenges. This is a major component of having a growth mindset, which is an important mentality to have especially to succeed in math class. I discussed the importance of having a growth mindset in my Week 2 post Growth vs. Fixed Mindset).

Learn Alberta. (2008, October 1). Effective portfolios [Snapshot].
Retrieved from http://bit.ly/2Am46dC

Therefore, portfolios in math class are important because they:

• are a powerful tool to assess as students learn,
• help students become in charge of their own learning, and
• foster a growth mindset.

Using the Right Kind of Graph to Show Your Data

From a young age, students are asked to show the data they have collected in various forms of charts, tables, graphs, and plots. With so many different ways to show your data, how do you know which one will be most representative and accurate of what you've found? Never fear, the data displayer is here!

There are three main ways we can show our data:

1. Using pictures of real objects - picture graphs and concrete graphs;

2. Using symbols - pictographs, tally charts and frequency tables;

3. Using abstract representations - bar graphs, stem-and-leaf plots, line graphs, scatter plots, circle graphs, box plots.

Since there are a lot more different ways to represent data abstractly, I will focus on these.

Bar Graphs

A bar graph is a chart that uses the length or height of bars to represent quantities, often the number of occurrences of particular responses. Bar graphs are used to display discrete data, meaning the data can only take certain values that can be counted. The number of possible values is also limited. A Maths Dictionary for Kids further expands on this definition.

Chela5808. (2009, January 1). Bargraph [Online Image]. Retrieved from http://wikieducator.org/File:Bargraph.jpg.

However, there are variations of bar graphs that do record continuous data; specifically, data that can be refined to be more specific. The Minitab Blog provides a good definition and some examples of both continuous and discrete data.

A histogram and stem-and-leaf plots are both examples of variations of bar graphs that represent continuous data. The categories along the horizontal axis are always continuous number intervals, and therefore the bars in this graph are touching to show this continuity. Stem-and-leaf plots are most appropriate when numerical data are best organized by place value. They show the number of occurrences of data in each interval as well as an individual piece of data. Examples of both are shown.

Statistics Canada. (2013, July 23). Example of a histogram [Online Image]. Retrieved from http://bit.ly/2zR5Nl2

Yale University. (2008, June). Example of a stem-and-leaf plot [Online Image].
Retrieved from http://bit.ly/2mE78H0

Line Graphs

Line graphs, also known as broken-line graphs, are used to show trends in data but connecting plotted points that are not in a straight line. The points are plotted to show how one variable is related to the other (Small, pp. 601). One of our variables is always continuous, typically time.

Markes, A. (2017, November 18). Example of a line graph [Graph].

Scatter Plots
Scatter plots are similar to line graphs in that they use the horizontal and vertical axes to plot points (Illinois Education). What's special about this type of graph is its purpose to show how much one variable is affected by the other. The closer the data points are plotted to make a straight line, the stronger the relationship between the two variables. Therefore, you would use this type of graph when you want to see a pattern, trend or relationship between the two variables.

Markes, A. (2017, November 18). Example of a scatter plot [Graph].

Circle Graphs

A circle graph is a circle that is divided into sections or categories. The main function of a circle graph is two-fold: (1) show the relationships among parts of a whole and (2) show the relationships between each part to the whole (Small, pp. 603). This graph is most often used when it is important to see how a total amount is distributed.

Statistics Canada. (2013, July 23). "Example of a circle graph" [Online Image].
Retrieved from http://bit.ly/2iufSeh

For any graph you create, make sure you include a meaningful title and label all axes and legends clearly so as to guide the reader in interpreting it accurately.

I don't trust people with graph paper; they're always plotting something.