Examining Health Risks

Context: This intermediate ESOL class has been meeting for several months at a local community college. None of the students have had formal schooling beyond the 8th grade. Although the teacher had conducted a goals survey in August to determine students’ individual needs and find out what they wanted to get out of the class, she hadn’t yet done much with the information. Now she wanted to revisit those goals in order to more clearly link her instruction to them. She used the role-related goals worksheet to start the process. Many of the goals from the earlier survey appeared again – learn English, more confidence, GED, better jobs, etc. 

As the class looked at the EFF Standards Wheel to talk about which skills related to their goals, they talked about their need for math and about how much they have to deal with numbers at work, from timesheets to company performance updates. When a student showed the teacher one of these updates, she saw that much of the information was presented in tables comparing production numbers over time, percent change, etc. Another student said that his employer gave them a monthly breakdown of absentee rates. Although their needs were different, all of the students felt a need for some work on math (the unemployed students felt that it connected to their long-range GED goals). Since they were ESOL students, there was no assessment information about their math abilities, so the teacher had to investigate what they already knew . She also needed to review the Use Math to Solve Problems and Communicate Standard, since it was not one she was familiar with. Then she needed to create a math/English lesson that was relevant to their need to read percents, decimals, or ratios at work. They had been studying health issues for the last couple of weeks, so she decided to use this as a segue by talking about health and safety risks, at work and elsewhere.

Lesson:

First the teacher had the students look up the word “risk” in the dictionary and discuss its meaning.  Then she explored what they knew about the mathematical concepts involved in determining risk, such as the meaning of ratios - 1 out of 8, 1 in 6 million, etc. The students were able to identify low and high risk without confusing the larger numbers as a sign of greater risk.

The teacher asked the students what the purpose of learning about risk ratios might be, and this reminded them of a discussion they had had during their health unit about the panic over SARS, even though the risk of contracting it was actually very low for most people. They talked about how this kind of information can help you determine how serious a risk is.

To begin practicing, they examined the statistics from a N.Y. Times article (below), and worked with a partner to create a chart that ranked these risks from greatest to least. They also discussed whether the things people worry about are necessarily high risk or are perhaps just high in our consciousness due to news reports and public interest. 

Risk

Odds of injury requiring medical treatment

Number of newspaper articles written last summer (the “Fear Index”)

Skin Cancer

1 in 200

102

Food Poisoning

1 in 800

257

Bicycles

1 in 1,700

233

Heat exposure

No reliable statistics for injuries

229

Children (14 and under) falling out of windows

1 in 12,800

89

Fireworks

1 in 32,400

59

Drowning (while boating)

1 in 64,500

1,688

West Nile Virus

1 in 68,500

2,240

Shark attacks

1 in 6 million

276

Information taken from “Never Bitten, Twice Shy: The Real Dangers of Summer," The New York Times, 8/9/03

Once they had ranked the information, they compared their charts and discussed how they arrived at their sequences.

Next, they brainstormed some risks they were actually concerned about, from the risk of World War III to INS raids to earthquakes to terrorist attacks. They discussed the fact that not all risks can be calculated because you might not have enough information. They figured out that in order to calculate the risk ratio you need to know: a) the total number in the population you’re talking about – a community, a workplace, a state, etc. and b) the number of people in that community that are affected by the risk. For example, to figure out the risk of being injured in a car accident, they determined that you’d need to find out how many people in the state were hurt in car accidents last year in relation to the total population of the state.  With that understanding, they went back to the brainstormed list to figure out which risks they would be able to determine and which they couldn’t get enough information about.

Then the teacher asked if anyone knew how to express 1 out of 8 as a percent. They all seemed to understand that it could be done, but didn’t know the process.  Then, suddenly, one student came up with 12%.  The teacher asked him how he had arrived at that figure and he explained that he knew ½ was 50%, so ¼ must be ½ of that or 25%, and 1/8 must be ½ of that or about 12%. When she asked about changing 1 out of 6 into a percent, another student explained that the way he did it was to think of a pie divided into 6 parts.  He knew that if the parts were each 15%, the 6 parts would add up to 90%, so 15% was not large enough.  He knew that 16% would add only 6% more to the 90% for a total of 96%, so the answer had to be closer to 17%. Both of these were wonderful examples of how adults may lack the knowledge to perform a mathe­matical operation but still understand the concept and be able to arrive at the answer. The teacher praised the creative strategies, but some students protested that these weren’t the exact “right” answers, and this led to a discussion about the value of estimation. For the purpose of evaluating the risk, were these numbers close enough? When do you need to calculate precisely and when will estimation suffice? What are some things that we estimate and what math do we use to do it?

In the next class, the teacher taught them the algorithm for converting ratios/fractions to percents (for the times we need to be precise) and they practiced converting the ratios they had worked with the day before.

Algorithm: Divide the numerator by the denominator and move the decimal point two places to the right (e.g. 1/3 or 1:3 = 1divided by 3 = .33333 etc. Move the decimal two places to the right and you have 33%.

Then she handed out short informational texts she had found about some of the topics on their brainstormed list of concerns and gave them this assignment:

1) Select one topic to read about and extract the risk data.

2) Convert and organize the data into the two common formats (1 in x, % at risk), deciding how precise the percent needs to be (they decided to round to the tenth of a percent).

3) Add your information to the class chart so that everyone can compare the risks.

The data came in a variety of formats:  There is a 32% chance that a woman will develop varicose veins in her lifetime, but a 1 in 8 chance that she will develop breast cancer. The prevalence of diabetes in the United States is 6.2% across all cultures, but it affects 1 in 6 people of Hispanic/Latino background.  The class spent some time talking about these different ways of stating risks and practiced converting the information between the two formats.

Class chart

Health concern

1 in x

% at risk

Breast cancer

1 in 8

12.5 %

Alzheimer’s over 65

1 in 10

10%

etc.

   

Since, throughout the lesson, they had been talking about their processes for arriving at their answers, it was not too difficult for them to help the teacher come up with an assessment checklist for their assignment. She asked them, “How will we know if you’ve done this well?” and, together, they came up with most of the ideas she used in the checklist .

Assessment Checklist

Name ______________________________         Date _____

I observed that you were able to:

     1. ____  Take the correct numeric information from text

     2. ____  Make calculations correctly

     3. ____  Round numbers correctly

     4. ____  Explain the procedures you used

     5. ____  Place numbers correctly in the chart as ratios and ercents

     6. ____  Identify when/if necessary information was missing

The teacher watched and recorded the students’ activities in an observation log as they worked in pairs to interpret and select the data, use their mathematical knowledge to organize the data, agree upon an appropriate level of precision, check their work and make revisions when the results were inappropriate, and produce a chart representing their findings. She had worried that the students would struggle through the English information, but they did well at picking out the data they needed. She wondered, “Could it be that because English language learners focus on the words they do know, they have natural skimming or scanning skills?”

After the chart was completed and discussed, they talked about how the activity helped them appreciate the importance of paying attention to statistics so that they could make informed decisions based on information rather than media hype . Because they now understood how to compare relative risks, they'd be able to distinguish between undue concern about relatively minor risks (e.g. contracting SARS) and more significant risks that they could address with behavior changes (e.g. washing hands regularly to avoid illness). And, although they had not really noticed it happening, they got a lot of English practice as they read and discussed their findings. The students felt that the lesson would also help them understand the statistics they were asked to read at work.

This lesson had made the class think more about health and safety risks at work, and some students wanted to learn more about the risks specific to their jobs (poultry processing, stitching, lifting, etc.). They had many stories to share about workplace injuries and decided that they would like to write about these in English.

Here is how the “Use Math to Solve Problems and Communicate” Standard was addressed in these lessons.

Use Math to Solve Problems and Communicate
How the Standard was Addressed

Understand, interpret, and work with pictures, numbers, and symbolic information.

Students learned how to identify the information needed to calculate risks, and to find and interpret this data in a number of different sources. They learned to understand the meaning of risk ratios written as both “1 in x” ratios and as “% of” prevalence. 

Apply knowledge of mathematical concepts and procedures to figure out how to answer a question, solve a problem, make a prediction, or carry out a task that has a mathematical dimension.

Students used their understanding of proportion and ratios to rank the risk ratios in order from greatest risk to lowest risk.  They converted ratios/fractions to percents, correctly using multiplication and division.  They used their understanding of percents and fractions and their own algorithms, “discovered” methods, or teacher-suggested methods to accomplish this task.

Define and select data to be used in solving the problem.

Students selected data from a variety of written sources in a variety of formats.

Determine the degree of precision required by the situation.

Students observed the degree of precision used in the information they were reading and decided that rounding to the half percent was the degree of precision they needed.

Solve problem using appropriate quantitative procedures and verify that the results are reasonable.

Students used a variety of strategies to arrive at their results and to check their answers.  (e.g. They compared the ratios and their accompanying percents to see if an answer seemed reasonable.) They also compared and discussed their calculations.

Communicate results using a variety of mathematical representations, including graphs, charts, tables, and algebraic models.

Students together created a risk chart (both by ratios and percents) and used this information to reassess their own concerns.