The Life and Times of a CCA Teacher

Excellent Students #1, 2, 3

Introduction

• We did a survey on teachers

• Why? In order to learn about teachers’ views, rather than the students’, which we already have a general idea about.

• Survey sent to a random sample of CCA teachers

• Covered a number of different topics, relating primarily to education.

SRS

• Listed teachers in alphabetical order 1 —78

• Used Table B to acquire two digit numbers randomly

• Numbers >78 and repeats weeded out.

• 30 teachers used for SRS, 10 backups were sent out as well

Literature Review Facts

• In the US, the average student:teacher ratio is 15.5 students per teacher, varies with each state. In CCA, though, the student:teacher ratio is 34:1.

• About 88% of secondary teachers nationwide have at least a bachelor’s degree, while about 50% held a degree higher than bachelor’s

• Average amount of teaching experience for a secondary teacher was about 17-18 years of teaching.

Question 1: What department do you teach in?

• No teachers in the social studies or PE departments responded to our survey.

• Math, English, and Envision comprised the largest part of the sample.

• It doesn’t seem like teachers in any particular department are less amenable to taking surveys; we’ll talk more about this later.

Question 2: For how many years have you been teaching high

school?• The sample mean was

6.389, while the median was 5 – when the mean is greater than the median, the sample is skewed right, as can be seen from the histogram.

• Every teacher in the sample had less experience than the national average (17 years), which is to be expected, since CCA is a new school.

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5

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9

1-3 4-6 7-9 10-12 13-15

Question 3: How many high schools have you taught at?

• By a large margin, the mode for this question was 2.• Why? Most of the teachers were probably recently

transferred from another school within the district.

# of high schools

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1 2 3 4 5

Resp

on

ses

Question 4: List all college degrees that you have obtained.

• A majority of teachers in our sample achieved the BA college degree. BS, MA, and M.Ed degrees were achieved in smaller proportions, and only one each had an MS or PHD.

• 17/18 = 94.5% of responders had some degree, compared to an 88% national average.

• “Other” responses included M.Phil, AA, BFA, and 2 BAs.

AP Statistics Final Project

List all college degrees that you have obtained.

Answer Options

Response Frequency

Response

Count

BA 64.7% 11

BS 29.4% 5

MA 47.1% 8

MS 5.9% 1

M.Ed 23.5% 4

PHD 5.9% 1

List all others: 5

answered question 17

skipped question 1

Question 5: Why did you choose to become a high-school teacher? (Check

all applicable.)Why did you become a high-school teacher?

02468

10121416

I needed themoney.

I liketeaching.

I like teens. I wanted tomake a

difference.

I loveliterature.

Question 6: Why did you choose to come to CCA?

• There were two other choices on the survey itself: “I needed the money, and the district happened to hire me,” and “I had colleagues at CCA.” Neither of these was ever chosen.

Answer OptionsResponse Frequency

I liked the ideas the school was built on.

44.4%

I needed the money and the school district happened to hire me at the right time.

0.0%

I had colleagues at CCA.

0.0%

I didn't. CCA sought me out.

27.8%

Other (please specify)

27.8%

Question 7: Rate the overall quality of the following aspects of CCA.

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Very low Low Medium High Very high

Rating

# o

f R

es

po

ns

es

ASB

Envision

Class choice diversity

Question 8:As a high school student, how

often did you...

• Most teachers admitted to at least occasionally procrastinating, 1/3 said often

• Most teachers either played sports “All the time” or “Never,” with no “Sometimes” responses.

• The teachers on the most part had fairly positive reviews of their high school experience.

How often did you...

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12procrastinate in meetingdeadlines?

play sports?

enjoy being in school?

Question 9: During classtime...Items allowed in class

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Water Food Drinks otherthan water

Personalmusic

players (i.e.iPods)

Cell phones Laptops

Type of Items

Num

ber

of It

ems

which of the following do you allow yourstudents to have in class? which of thefollowing do you allow your students to havein class?

which of the following do you, personally,have? which of the following do you,personally, have?

Question 10: On average, how many students do you teach per class?

• The average number of students in a classroom in our sample was 33 kids.

• We saw earlier that the CCA average was 34 students:teacher, so our sample isn’t much different from this.

Question 11: On average, how many hours per week...

• On average, teachers claimed to spend 3.28 hours more than their students on work.

• However, upon reviewing the question, a discrepancy appears– first question asks teachers to

give the time they spend grading all student work

– second question asks for the average time spent on just homework

Answer Options

Response

Average

do you spend grading student work?

7.56

do your students spend doing homework from your class?

4.28

Question 12: Per week, CCA students spend...

• It’s a bit worrisome that, on average, the teachers at CCA believe students don’t spend enough time doing homework

• On outside activities, most teachers thought that the students spend the right amount of time on extracurriculars and very few do not spend enough time

• In other words… CCA teachers think we sleep too much. Hmm.

Answer OptionsNot enough

time

The right amount of

timeToo much

timeRating Average

...on homework. 7 7 4 1.83

...on extracurricular activities.

2 12 4 2.11

Question 13: Overall, how satisfied are you with teaching at CCA?

• The results for this question were very skewed to the left (which is good).

• Only one teacher responded that they were at all unsatisfied.

Answer Options

Unsatisfied

Somewhat

unsatisfied Neutral

Somewhat satisfied Satisfied

I am... 0 1 1 4 12

Confidence Intervals• μ = average hours/week grading homework• Normality: n = 18 < 30, so we cannot use Central

Limit Theorem to say that since the sample size is large enough, we can assume a roughly Normal sampling distribution. The histogram below also obviously shows a right skewed distribution. Since there are no major outliers, it is safe to assume normality as long as well proceed with caution that these results may not be completely accurate.

• Independence: 10n ≤ N 10(18) = 180 ≤ N There are less than 180 teachers at CCA. Proceed with caution

• SRS: This is an SRS.

• There is 95% confidence that the real average hours/week grading homework is between the interval

)9.378662,5.732449(

183/3.665775292.110 67.55555555/*

nstx

)9.378662,5.732449(

Ti me Spent Gradi ng

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3 6 9 12 More

Hours/ WeekFr

eque

ncy

Frequency

Two-Variable Stats

• We had a number of hypotheses as to how different variables might be related. For instance, we figured that the amount of time a teacher spent grading student work would be more or less proportional to the amount of time students spent doing it.

• x = hours/week spent grading work• y = (hours/week)/student spent doing homework• r = .253• ŷ = 2.947 + 1.76x• r2 = .064 is very low, so there is not a strong

correlation between hours/week spent grading homework and (hours/week)/student spent doing homework, which is pretty weird.

Two-Variable Stats• Displayed left is a two-way

table of the responses to parts B and C of Question 8. (None of the teachers responded “Never” when asked how often they enjoyed being in school.)

• Using conditional probability, we can analyze the table

• E.g. “Often” or “All the time” given that they never played sports was 4/5 = 0.8, while the probability that they did so given that they played sports often was 7/10 = 0.7 fairly close, not large impact

Enjoyed High School

　 Occasionally /Sometimes

Often/Always Total

Never 1 4 5

SportsOccasionally/Sometimes

1 2 3

Often/All the time

3 7 10

Total 5 12 17

Chi-Squared: Response Rate by department

• One thing we knew would be a factor from the beginning was voluntary response.

• Despite measures taken to improve it (aka guilt-tripping and begging), we still got a measly 45% response rate. We decided to statistically analyze this to see which teachers to blame.

• Chose to analyze the possibility that a teacher’s department affected the likelihood that they would respond to the survey, i.e. math teachers more likely since they would appreciate the purpose of the survey more.

Response Rate/Chi-Squared

• Our hypotheses are – H0: the distribution of survey

responders is the same as the distribution of the SRS by department, and

– HA: At least one of the listed proportions is significantly different.

• The chi-squared test requires that all expected values be above 1 and no more than 25% below 5, so we proceed with caution.

Department Observed Expected (o-e)2/e

Math 5 6 0.028

English 4 3 0.111

World Languages

2 4.5 1.389

Special Ed. 1 2.25 0.694

Science 2 3 0.111

Social Studies

0 0.75 0.75

PE 0 2.25 2.25

Envision 4 8.25 2.189

　χ2 = 7.522

• We have 8 categories, so we use the chi-squared distribution with df = 7

• P(chi2 > 7.522) = .377

• This is a very high P-value, meaning that there is no significant deviation from the expected values. We fail to reject the H0 that no department’s teachers are more or less likely to respond.

Response Rate/Chi-Squared

Significance Tests

Question 10

• T-significance tests were done to see whether or not the sample proved that CCA student: teacher ratio did not follow the previously found statistics and were statistically significant evidence that the previous statistics do not apply to the current CCA the average student: teacher ratio.

• μ = average student: teacher ratio• Normality: n = 18 < 30, so we cannot use Central Limit Theorem The

histogram above also obviously shows a left skewed distribution. T-tests are fairly robust, so we have normality as long as no outliers are present.

• Independence: 10n ≤ N 10(18) = 180 ≤ N There are fewer than 180 teachers at CCA. Proceed with caution

• SRS: This is an SRS.

Average Student: Teacher Rati o

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Average Student: Teacher Rati o

Freq

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Frequency

• H0: μ = 21.3 HA: μ ≠ 21.3

• The p-value <.05 so we can reject the null hypothesis. Therefore we can safely conclude that there is strong evidence that the average student: teacher ratio at CCA is not 21.3:1, which the average student: teacher ratio is in the California.

Significance TestsQuestion 10

05-5.51687E)17,65.3308668265.33086682(1

65.33086682189.311599/

1533

/0

dftPns

xt

Discussion• Teachers were a bit unconcerned with the trivial

matters of students outside their own classroom less than half our sample responded

• We could not assume normality of our sample using the Central Limit Theorem (sample size must be at least 30)

• Because of the small sample size, we may have not been able to notice correlations more prominent in a larger sample

• The survey questions were all well thought-out and collaborated upon

Conclusion

• Throughout this project, we both exercised our statistical skills and learned more about the opinions of our fellow teachers

• We developed an informative survey of our sample of teachers, most of which didn’t reply

• Our results were informative

Bibliography

• Kohn, Brian. "Canyon Crest Academy School Profile." 18 Jan. 2009 <http://teachers.sduhsd.net/cccounseling/documents/0809CCAprofile.pdf>.

• "Pupil/Teacher Ratio (most recent) by state." StateMaster - US Statistics, State Comparisons. 18 Jan. 2009 <http://www.statemaster.com/graph/edu_ele_sec_pup_rat-elementary-secondary-pupil-teacher-ratio>.

• “Public Secondary School Teacher Survey on Vocational Education.” 18 Jan. 2009 http://nces.ed.gov/surveys/frss/publications/94409/