The Life and Times of a CCA Teacher

1
The Life and Times of a CCA Teacher

• Excellent Students 1, 2, 3

2
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.

3
SRS

• Listed teachers in alphabetical order 1 78
• Used Table B to acquire two digit numbers
  randomly
• Numbers gt78 and repeats weeded out.
• 30 teachers used for SRS, 10 backups were sent
  out as well

4
Literature Review Facts

• In the US, the average studentteacher ratio is
  15.5 students per teacher, varies with each
  state. In CCA, though, the studentteacher ratio
  is 341.
• About 88 of secondary teachers nationwide have
  at least a bachelors degree, while about 50
  held a degree higher than bachelors
• Average amount of teaching experience for a
  secondary teacher was about 17-18 years of
  teaching.

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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 doesnt seem like teachers in any particular
  department are less amenable to taking surveys
  well talk more about this later.

6
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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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.

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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 AP Statistics Final Project AP Statistics Final Project
List all college degrees that you have obtained. List all college degrees that you have obtained. 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 List all others 5
answered question answered question 17
skipped question skipped question 1
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Question 5 Why did you choose to become a
high-school teacher? (Check all applicable.)
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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 Options Response 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
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Question 7 Rate the overall quality of the
following aspects of CCA.
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Question 8As 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.

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Question 9 During classtime...
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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
  studentsteacher, so our sample isnt much
  different from this.

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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
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Question 12 Per week, CCA students spend...
Answer Options Not enough time The right amount of time Too much time Rating Average
...on homework. 7 7 4 1.83
...on extracurricular activities. 2 12 4 2.11

• Its a bit worrisome that, on average, the
  teachers at CCA believe students dont 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.

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Question 13 Overall, how satisfied are you with
teaching at CCA?
Answer Options Unsatisfied Somewhat unsatisfied Neutral Somewhat satisfied Satisfied
I am... 0 1 1 4 12

• The results for this question were very skewed to
  the left (which is good).
• Only one teacher responded that they were at all
  unsatisfied.

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Confidence Intervals

• µ average hours/week grading homework
• Normality n 18 lt 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

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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
• y 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.

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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 Enjoyed High School
Occasionally /Sometimes Occasionally /Sometimes Often/Always Often/Always Often/Always Total Total
Never Never 1 1 4 4 4 5 5
Sports Occasionally/Sometimes Occasionally/Sometimes 1 1 2 2 2 3 3
Often/All the time Often/All the time 3 3 7 7 7 10 10
Total Total 5 5 12 12 12 17 17
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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 teachers
  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.

22
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
?2 7.522
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Response Rate/Chi-Squared

• We have 8 categories, so we use the chi-squared
  distribution with df 7
• P(chi2 gt 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
  departments teachers are more or less likely to
  respond.

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Significance TestsQuestion 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 lt 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.

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Significance TestsQuestion 10

• H0 µ 21.3 HA µ ? 21.3
• The p-value lt.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 21.31,
  which the average student teacher ratio is in
  the California.

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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

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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 didnt reply
• Our results were informative

28
Bibliography

• Kohn, Brian. "Canyon Crest Academy School
  Profile." 18 Jan. 2009 lthttp//teachers.sduhsd.net
  /cccounseling/documents/0809CCAprofile.pdfgt.
• "Pupil/Teacher Ratio (most recent) by state."
  StateMaster - US Statistics, State Comparisons.
  18 Jan. 2009 lthttp//www.statemaster.com/graph/edu
  _ele_sec_pup_rat-elementary-secondary-pupil-teache
  r-ratiogt.
• Public Secondary School Teacher Survey on
  Vocational Education. 18 Jan. 2009
  http//nces.ed.gov/surveys/frss/publications/94409
  /