Arizona
The Arizona Adult Education Mathematics Standards are guided by NCTM’s Process Standards, including Communication, Connections, and Problem-solving.
Please share a story about how you saw or heard this core concept come alive for students during the Data and Graphs lessons.
I gave my students homework before we began Lesson 4. They had to ask 4 people two yes/no questions and then bring the data back to class the next day. When they came back to class they then had to arrange the data in a table to show the names of the people and their answers.
This was difficult for 2 students. They didn’t understand the concept of arranging and organizing the data to show what it represented. A student who had made a very nicely organized table began to explain her process of organization for the data. She began to work and discuss how to set it up with the 2 who didn’t quite understand. It was a great moment of communication between students. This student even got up and went to the whiteboard to show the possible ways of organizing the data.
The “Clothes In My Closet” activity generated discussion among the group members. First we made a frequency chart, followed by a continent chart—where each country name was placed in a continent. When I asked, “Where is Peru?” A student answered, “In Mexico.”
The classroom (actually a computer lab) has a world map on a wall and a globe. Students wanted to know where to locate Mauritius and Lesotho. A challenge for me occurred in where to place the country of Jordan on the continent chart.
Student observations:
- Not one of my clothing is made in the USA.
- 5 out of 8 articles of clothing is made out of 97% or 100% cotton fiber.
- I’ve never heard of these countries.
Throughout the EMPower lessons, we’d spend time stopping and communicating about the data and our processes. Students would communicate, in writing, by answering the questions in the book for each lesson. Afterwards, we’d have a class discussion to share out answers. When students got stuck or confused, I’d ask probing questions (sometimes rewording similar questions multiple times) to try to get the students to answer their own questions. During whole class discussions, and one-to-one talks, I observed that talking aloud really helped many of the students to “get it”. For example, I’d reword “50%” as “half” (or they would) and with the manipulatives/activities they’d “see” the value of 50% and how that is the same as half. I noticed that by communicating in one large group, and talking about the activity, they’d learn a lot from their peers. It seemed communication came alive during our class—and greatly enhanced both learning and mathematical understanding.
Please share a story about how you saw or heard this core concept come alive for students during the Data and Graphs lessons.
During our Data and Graph sessions I saw students actually see and create physical representation of the number that were derived fractionally decimally and percentage wise. Some began to gain some sense of numeracy. Before the numbers were just symbols to be manipulated. These exercises helped them to really see through color, art and in so doing the connects between the symbols and real world. We analyze kilowatt usage on power bills, mortgage amortization (on Excel), weather and temperature patterns, and international trade in regard to clothing. We did polls on the death penalty. We did a survey on the popularity of the presidential incumbent. There were so many “connections” that could be demonstrated.
I have a student named S__ in my evening GED class who is a fairly low level learner. She can, however, complete most adding/subtracting/multiplying and dividing problems. While working on Lesson 7 in the EMPower (Data and Graphs) book, A Mean Idea, it was fascinating to see her make a mental leap in her thought process.
She had been figuring out means from a data set and began asking questions regarding whether the data was going to be accurate. By this she meant whether it was a solid representative sample of the population in order to be classifying a group in a certain way, e.g., stereotyping families as watching to[sic] much TV when you are only looking at 5-10 families. She said that if you want accuracy, you should consider a million families.
This lesson triggers connections between literacy and numeracy. A nineteen year old male student studied the paragraph of many words on page 66 of Practice: How Does It Go? and sat back in his chair, darting a quick glance in my direction. “I’m going to draw a line and that line is going to stand in the place of all those words, isn’t it?” I grinned and said, “Yes, it is.” The student decided to graph 2 graphs one for
He darted another quick glance in my direction and said, “Two stories require 2 lines, don’t they.” It was more of a statement than a question. “Yes, did you see 2 stories there?” “Yes. It would have been difficult for some of the students to have seen the 2 stories.” “Yes, I think so, too.” “You’re going to have to use numbers for words. That’s what this is all about, isn’t it?” “Math is a wonderfully concise language, “ I replied. “It’s a language that opens many, many doors to very exciting worlds.” “Math is not just a language, it’s art. I’ve drawn a picture.” “Yes, and later when you go to college, you’ll find math is music.” “Then, is math all things?” “There are some who say it is.”
In doing the graphing math with the students, a lot of “real life” came to light. During one lesson we talked about elevators in detail after looking at a bar graph showing elevator use and another one showing number of elevators in different countries.
We went on to calculate from the graphs how many people would have to wait in line to get on an elevator. In the US it was around 5 hours, but in Italy it was only 2 ½ hours.
Another lesson dealing with categorizing food brought about a lot of conversation about health and nutrition.
In general, the students are connecting their math use to other topics and how it might affect them personally.
Please share a story about how you saw or heard this core concept come alive for students during the Data and Graphs lessons.
When I asked the students to look through our class city newspaper for data that they could organize they selected the weather page and the food advertisements. We talked about data from those pages. As a class project we decided to focus on food (a natural digression from Chapter 2 in the book).
The students worked in teams to decide on categories of products in an advertisement. We also discussed nutritional values and costs. Students narrowed the options by analyzing product types. The problem solving aspect came from 1) refining categories within each work group in the class 2) finding percentages of representation among foods advertised 3) predicting why some categories were more prevalent than others in the ad.
I gave students a chart that was only partially filled in (number, fractional part, percent, benchmark %) and asked them to complete the chart and draw the circle graph.
One of the items not filled in was a percent -- It happened to be the only percent not calculated. It also happened that the number was one that was found elsewhere on the chart…with its %. I figured students would either not see the other number and calculate the percent as done in class (they were given calculators) or notice the other number and duplicate the %. But instead they added up the other %’s to find out what was missing…and wanted to know if that was the correct way to do it. I was quick to point out that there were many ways to get the correct answer.