Stimulating Understanding of Computational science through Collaboration, Exploration, Experiment, and Discovery for students with Hearing Impairments
a collaboration of the Shodor Education Foundation, Inc., Eastern North Carolina School for the Deaf, Barton College, the National Technical Institute for the Deaf, and Interpreters, Inc.

For Teachers!

How does your hair know how long to grow?

Notes on teaching the lesson: The students are learning on two levels in this lesson. First, they are learning how our bodies regulate the length of our hairs. Hairs grow for a length of time, rest and then fall out. The length of a type of hair depends on the rate of growth times the length of time it grows. If you cut your hair the cut hairs will be shorter when they stop growing. Hairs that were too short to be cut or hadn't started growing yet will reach the maximum length and stop growing. 

Second, they are learning how scientists learn by asking questions. Two types of questions are emphasized in this lesson: verification and validation. These are different ways to check if the answer is correct. Verification is checking that we followed the directions correctly: If you do what I did, will you get the same answer? For instance, 2+2 = 4. You can verify that with a calculator. Validation asks if the procedure was reasonable or correct: Did this situation call for addition and not subtraction? Scientists need to be careful with what they are doing, and they need to be careful with why they are doing it.

The following are the student pages. Answers and suggestions for the teacher are in BLUE.

Teacher Support 

Answers to questions.

Hair Science page

A single hair has a thickness of 0.02-0.04mm. How many hairs next to each other would you need to equal one millimeter? 25-50 hair fibers next to each other make one millimeter.

0.02mm X 50 = 1mm, 0.04mm X 25 = 1 mm



Math page

There are really 365.25 days in a year if you consider leap year. Is it important to include that in our calculation? The longest a hair can grow is 8 years. The average person's longest growing hair only grows 4 or 5 years. Scalp hairs grow .44 mm/day. 

.25days/year X .44 mm/day X 8 years = .88 mm. The biggest difference leap year can contribute is less than 1 mm. For most people it is even less than that. This probably isn't significant as a single factor. If the model grows in complexity and additional factors are added with their own inherent errors, the errors can add up. This cumulative effect could become a problem. 


How many years would your scalp hair need to grow to be 60 cm long? About 45 months or 3.75 years

How many years would your scalp hair need to grow to be 90 cm long? About 67 months or 5.58 years

How many months would it take to grow a beard of 15 cm? 12.46 months 1.04 years



Science Extension page

Lets revisit the data. The literature says that everyday 40 to 100 scalp hairs fall out. We have about 100,000 scalp hairs. How long would it take for all of them to fall out? 100,000/40 = 2,500 days or 6.85 years 100,000/100 = 1,000 days or 2.74 years

Science Enrichment page

The graph plots the length of the hair with the hair's number.  I measured 100 hairs and put the measurements in a spreadsheet. (Download the
Excel spread sheet.) and gave them numbers 1-100. I next sorted the data by the length column. That gave the longest hair the number 1 and the shortest hair the number 100. Then I plotted the length versus the hair number so I could see how the range varies. I plotted the data this way to find a pattern. Given the results, can we derive additional information from the graph? Can we conclude that hair number one has the fastest growth rate? Yes. The slope of the line from 1 to about 85 is the rate at which the growth rate changes. 

Is the graph linear? No, but the graph appears to be a combination of 2 lines with a vertex at approximately 85. 

Why does the graph change direction at 85? I assert that the hairs above number 85 spent part of the time in telogen phase, i.e., they were resting during part of the months since I cut her hair. Hair 100 just started to grow again in March, so it is very short. Hair 86 started anagen (growing again) a few days after I cut her hair. 

Which explanation of growth rate does the graph support? I would argue that if hairs grow at a constant rate there would be a horizontal line for all of the hairs that were in anagen for the entire time since I cut her hair. There would also be a sloping line for hairs that spend varying lengths of time in telogen. There is no horizontal section on the graph so the hairs grow at different rates during different parts of the anagen phase. The data supports the statement that the hairs grow at different rates but it doesn't give us enough information to draw conclusions about how the rate changes. 

Our models assume a constant average growth rate. STELLA allows us to make the growth rate variable a function of the place the hair is in its growth cycle. Since the hair appears to grow fast when it is young and slower when it is long and old how would this affect the answer to our analysis of a braid's diameter? 

Have the students change the STELLA model to account for the varying growth rate. I haven't made these changes because my data is very preliminary. It needs to be replicated and improved by including the additional measurements mentioned in the criticisms. 

If you don't have STELLA at your school you can down load a free Version of STELLA. This version is exactly like STELLA except you can't save your models. You can start with my model and modify it. 

Have your students replicate my hair measuring experiment. Send us (at Shodor) their report and we will post it with this lesson. If you have a school web page, post the report yourself and we will link to your report. 

If you have STELLA at your school and made improvements to my model please email them to me so I can post them, or post them yourself and let me know so I can link to your page. 

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The Shodor Education Foundation, Inc.

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This project is supported, in part, by the National Science Foundation Opinions expressed are those of the authors and not necessarily those of the National Science Foundation.