CNM ANNUAL STUDENT LEARNING ASSESSMENT REPORT€¦ · Assessment Report Page 2 of 12 Last Revised 8/2018 PART 3: REPORT ON ASSESSMENT OF STUDENT LEARNING Assessment Method Type of

Assessment Report Page 1 of 12 Last Revised 8/2018

CNM ANNUAL STUDENT LEARNING ASSESSMENT REPORT Due to the Student Academic Assessment Committee by October 15

PART 1: REPORT INFORMATION

Report Year and Contact Information

2017-2018 David Heddens [email protected] 50267

Academic Year Contact Person CNM Email CNM Office Extension

Subject of this Report

MSE--GE_MATH--General Education Mathematics

PART 2: CONTEXT IN WHICH THE ASSESSMENT TOOK PLACE

Program/Area Highlights and Successes (Wherever applicable, include course completion rates, job placement outcomes, and licensing examination pass rates. See the program information dashboard

at https://livecnm.sharepoint.com/sites/Dashboards/SitePages/Program%20Information%20Dashboard.aspx (access restricted to CNM employees) and other reports at https://www.cnm.edu/depts/opie.)

For the majority of assessed SLOs, students performed well in General Education Mathematics during AY2017/18. Mean rubric scores exceeded the 2.00 benchmark with a few notable exceptions, primarily within MATH 1315 College Algebra. Despite the identified weaknesses in college algebra performance, the overarching efforts of the math department of necessity are now focused on developing the new General Education Model.

Changes Implemented During the Past Year in Support of Student Learning

Major changes are underway due to the implementation of the new General Education Model. Chiefly among them will be the new pedagogical focus upon and assessment of the essential skills of Communication, Critical Thinking, and Quantitative Reasoning.

https://livecnm.sharepoint.com/sites/Dashboards/SitePages/Program%20Information%20Dashboard.aspx

https://www.cnm.edu/depts/opie


PART 3: REPORT ON ASSESSMENT OF STUDENT LEARNING

Assessment Method Type of Assessment Tool

Population or Course(s) Assessed

Graduate Learning Outcome(s) Assessed

Mastery Level (E.g., “Minimum score of 3 on a rubric scaled 0-4” or “Minimum score of 75%”)

Targeted % Achieving Mastery Outcome

Standard Test Questions Direct & Internal MATH 1315 Use and solve various kinds of equations and formulas.

Mean Rubric Score of at least 2.00 on a scale 0-3

N/A Target not met

Standard Test Questions Direct & Internal MATH 1315

Write mathematical explanations using appropriate definitions and symbols.


N/A Target not met

Standard Test Questions Direct & Internal MATH 1315 Construct and analyze graphs and/or data sets algebraically.


N/A Target not met

Standard Test Questions Direct & Internal MATH 1315

Utilize appropriate problem solving skills within the context of mathematical applications.


N/A Target met

Standard Test Questions Direct & Internal MATH 1330 Perform hypothesis tests. Mean Rubric Score of at least 2.00 on a scale 0-3

N/A Target met


N/A Target partially met


N/A Target met

Standard Test Questions Direct & Internal MATH 1330 Present the concepts of probability distributions.


N/A Target met


Standard Test Questions Direct & Internal MATH 1330 Present the concepts of probability distributions.


N/A Target not met

Standard Test Questions Direct & Internal MATH 1330 Compute point and interval estimates.


N/A Target met

Summary of Assessment Findings

CNM Gen Ed Mathematics SLO#1 – MATH 1315 College Algebra – Standard Test Question 1

Course-Level SLO and Component #1c: Use the equation of a function to determine its domain, determine the difference quotient, calculate its

average rate of change, and to perform other function operations.

1. Determine the difference quotient, 𝑓(𝑥+ℎ)−𝑓(𝑥)

ℎ, for the function below.

𝑓(𝑥) =4

𝑥

Numerical

Assessment

Problem #1

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error

−4

𝑥(𝑥 + ℎ)

MATH 1315 Fall and Spring mean rubric scores were 1.62 (n=398) and 1.66 (n=431), respectively.


Course-Level SLO and Component 2e: Determine the inverse function of a one-to-one function from an equation, a set of ordered pairs and/or

from a graph and state its domain.

2. Determine the inverse of the function 𝑓(𝑥) = √𝑥 + 2 − 3. State the domain of 𝑓−1.


Numerical

Assessment

Problem #2

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Neither answer is

correct

One of the answers

is correct

Both answers are correct:

𝑓−1(𝑥) = (𝑥 + 3)2

− 2

𝐷𝑓−1 = [−3,∞)



Course-Level SLO and Component 3a: Sketch the graphs of linear, quadratic, higher-order polynomial, rational, absolute value, exponential,

logarithmic, radical, and piece-wise functions using a variety of techniques including plotting points, using properties of basic transformations of

functions, and by determining and/or using key characteristics of functions such as symmetry, end behavior, intercepts and asymptotes.

3. Graph the function 𝑓(𝑥) = − log2(𝑥 + 5). Label any asymptotes.

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7𝑥


Numerical

Assessment

Problem #3

0 1 2 3

Answer

Not answered or

non-mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error


CNM Gen Ed Mathematics SLO#2 and SLO#4 – MATH 1315 College Algebra – Standard Test Question 4

Course-Level SLO and Component 4a: Apply the knowledge of function families to identify the appropriate type of function to solve various

application problems.

4. Howard’s bank account balance doubles every 14 years. Which of the following functions would model the bank account’s balance over

time?

a. Logarithmic

b. Exponential

c. Polynomial

d. Radical

Numerical

Assessment

Problem #4

0 1 2 (Not a possible

rubric score)

3

Answer Not answered Incorrect Answer Not Applicable b. Exponential



CNM Gen Ed Mathematics – MATH 1330 Introduction to Probability and Statistics – Standard Test Question 1

Course-Level SLO and Component 6-1: Use the appropriate test (z-test versus a t-test, and one-tailed versus a two-tailed test; mean versus

proportion; one-sample versus two-samples) to determine the veracity of a hypothesized claim.

1. The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range

from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean

FICO score is lower than the cutoff of 720. She finds that a random sample of 70 people had a mean FICO score of 705 with a standard deviation of 83.

Can the economist conclude that the mean FICO score is less than 720? Use the α = 0.05 level of significance and the P-value method with the TI-84

calculator.

a. State the appropriate null and alternative hypotheses.

Numerical

Assessment

Problem #1a

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with

minor conceptual

or calculational

error

𝐻0: 𝜇 = 720

𝐻1: 𝜇 < 720


b. Compute the P-value. Round the answer to four decimal places.

Numerical

Assessment

Problem #1b

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error

𝑝 = 0.0675



c. Determine whether to reject H0.

Numerical

Assessment

Problem #1c

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error

Do not reject 𝐻0.



Course-Level SLO and Component 4-3: Calculate and interpret the variance, standard deviation, and expected value of the binomial distribution.

2. A national college researcher reported that 67% of students who graduated from high school in 2012 enrolled in college. Twenty-nine high school

graduates are sampled.

a. What is the mean number who enroll in college in a sample of 29 high school graduates? Round the answer to two decimal places.

Numerical

Assessment

Problem #2a

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error

𝜇𝑋 = 19.43

𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠


b. What is the standard deviation of the number who enroll in college in a sample of 29 high school graduates? Round the answer to four

decimal places.


Numerical

Assessment

Problem #2b

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error

𝜎𝑋 = 2.5322 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠



Course-Level SLO and Component 5-1: Estimate the value of a population mean and determine the associated confidence interval for a population

mean.

3. A sample of 316 patients between the ages of 38 and 82 were given a combination of the drugs ezetimibe and simvastatin. They achieved a mean

reduction in total cholesterol of 0.92 millimole per liter. Assume the population standard deviation is 𝜎 = 0.18.

Construct a 99% confidence interval for the mean reduction in total cholesterol in patients who take this combination of drugs. Round the answers to two

decimal places, if necessary.

Numerical

Assessment

Problem #3

0 1 2 3

Answer

Not answered or

non-

mathematical

‘attempt’

Mathematical

attempt but major

conceptual or

calculational error

Mathematical

attempt with minor

conceptual or

calculational error

(0.89 𝑚𝑖𝑙𝑙𝑖𝑚𝑜𝑙𝑒,

0.95 𝑚𝑖𝑙𝑙𝑖𝑚𝑜𝑙𝑒)



CNM Gen Ed Mathematics – MATH 1320 Survey of Mathematics – Custom Assessment Questions per Instructor’s Prerogative

Course-Level SLO#2 Use and solve various kinds of equations: Competency 1 Understand the purpose and use of appropriate formulas within a

mathematical application.

MATH 1320 Fall and Spring mean rubric scores were 2.42 (n=23) and N/A (n=0), respectively.


Course-Level SLO#2 Use and solve various kinds of equations: Competency 2 Solve equations within a mathematical application.



Course-Level SLO#2 Use and solve various kinds of equations: Competency 3 Check answers to problems and determine the reasonableness of

results.


Interpretation of Assessment Findings

During AY2017/2018, 829 students were assessed in MATH 1315 College Algebra, with 398 and 431 students arising from the Fall and Spring Semesters, respectively. Students were assessed solely during the final exam as opposed to over a series of midterms. Students were permitted scientific calculator usage (graphing calculators prohibited per departmental policy) on the assessment questions. Per policy, students were not permitted any variety of notes usage during assessment.

With a new battery of assessment questions, evidence indicates that during any given academic year’s assessment student learning outcome achievement is highly dependent on the component of the student learning outcome of interest being assessed. During academic years AY2015/16 and AY2016/17, College Algebra exhibited weakness in failing to meet the benchmark of 2.00 for Course-Level SLO#1 and Course-Level SLO#4. But academic year AY2017/18 exhibited weakness in all but Course-Level SLO #4. Instead of concluding a decline in student performance across SLO’s #1, #2, and #3 it is the case that Course-Level SLO’s are large enough in scope to present strength in some of their components and weakness in others. There likewise may not be reason to conclude an improvement in student performance regarding Course-Level SLO#4. See Table 1 below for the specific mean rubric scores.

Table 1. MATH 1315 College Algebra mean rubric scores of assessment questions AY2017-2018 by Course-Level SLO and Component.

Course-Level SLO#1: Use and solve various kinds of equations and formulas Fall Spring

c) Use the equation of a function to determine its domain, determine the

difference quotient, calculate its average rate of change, and to perform other Q1 1.62 1.66

function operations.

Course-Level SLO#2: Write mathematical explanations using appropriate definitions Fall Spring


and symbols

e) Determine the inverse function of a one-to-one function from an equation, Q2 1.62 1.87

a set of ordered pairs and/or from a graph and state its domain.

Course-Level SLO#3: Construct and analyze graphs and/or data sets algebraically Fall Spring

a) Sketch the graphs of linear, quadratic, higher-order polynomial, rational,

absolute value, exponential, logarithmic, radical, and piece-wise functions using Q3 1.65 1.51

a variety of techniques including plotting points, using properties of basic

transformations of functions, and by determining and/or using key characteristics

of functions such as symmetry, end behavior, intercepts, and asymptotes.

Course-Level SLO#4: Utilize appropriate problem solving skills within the context of Fall Spring

mathematical applications

a) Apply the knowledge of function families to identify the appropriate type of Q4 2.27 2.37

function to solve various applications problems.

During AY2017/2018, 817 students were assessed in MATH 1330 Introduction to Probability and Statistics, with 354 and 463 students arising from the Fall and Spring Semesters, respectively. Fifty-three percent of students were permitted the use of notes during assessment, while 86% of students used a graphing calculator during assessment.

Introduction to Probability and Statistics students exceeded the benchmark for 9 of the 12 mean rubric scores, evincing adequate to strong student performance. However, it appears that computing the standard deviation of a binomial random variable may be problematic (question Q2b). Collectively, the academic years AY2015/16, AY2016/17, and AY2017/18 suggest strong student performance within MATH 1330. Table 2 presents the mean rubric scores of AY2017/18.

Table 2. MATH 1330 Introduction to Probability and Statistics mean rubric scores of

assessment questions AY2017-2018 by Course-Level SLO and Component.

Course-Level SLO#6: Perform hypothesis tests Fall Spring

1) Use the appropriate test (z-test versus a t-test, and one-tailed versus Q1a 2.46 2.51

a two-tailed test; mean versus proportion; one-sample versus two-samples) Q1b 1.76 2.09

to determine the veracity of a hypothesized claim. Q1c 2.09 2.22

Course-Level SLO#4: Present the concepts of probability distributions Fall Spring


3) Calculate and interpret the variance, standard deviation, and expected Q2a 2.02 2.32

Value of the binomial distribution. Q2b 1.29 1.64

Course-Level SLO#5: Compute point and interval estimates Fall Spring

1) Estimate the value of a population mean and determine the associated Q3 2.06 2.24

confidence interval for a population mean.

MATH 1320 Survey of Mathematics continues to exhibit strong student performance. Twenty-three students were assessed during AY2017/18. Due to the varied topics coverage across sections of MATH 1320, faculty custom designed their own assessment questions, and timing and circumstances of administration were at instructors’ discretion.

Performance on Course-Level SLO#2 was strong across the board with all 3 out of 3 mean rubric scores exceeding the benchmark of 2.00, as summarized in Table 3 below.

Table 3. MATH 1320 Survey of Mathematics mean rubric scores of

Assessment questions AY2017-2018 by Course-Level SLO and Component.

Course-Level SLO#2: Use and solve various kinds of equations Fall Spring

1) Understand the purpose of and use the appropriate formulas within Q1 2.42 N/A

a mathematical application.

2) Solve equations within a mathematical application. Q2 2.26 N/A

3) Check answers to problems and determine the reasonableness of results. Q3 2.24 N/A

Action Plan in Support of Student Learning (Describe changes to be made that are based at least in part on the assessment interpretation. If the assessment did not yield useful information, describe

changes to be made in the assessment methodology and/or criteria.)

MATH 1315 College Algebra continues to exhibit weakness in its Course-Level SLO’s. However with the new General Education Model in development, such weaknesses are not likely to be addressed during the next academic year and instead likely will be taken up during AY2019/20. Across all of the general education mathematics courses and SLOs assessed, students are performing well with a substantial majority of mean rubric scores exceeding the benchmark.

Please select all of the following that characterize the types of changes described in the above action plan:

☒ Assessment criteria revision ☒ Assessment methodology revision ☐ Assignment revision

☐ Budgetary reallocation ☐ Change in teaching approach ☒ Course content revision

☒ Curricular Revision ☐ Faculty training/development ☐ Process revision


Recommendations, Proposals, and/or Funding Requests Budget Needed

None. None.

PART 4: REMAINING YEARS IN CURRENT ASSESSMENT CYCLE PLAN (including any revisions) – OR -- UPCOMING ASSESSMENT CYCLE PLAN (if this was the final year)

Years of Full Cycle Next Year’s Assessment Focus (Describe how the next planned assessment is expected to provide information that can be used toward improving student learning.)

AY2019/20 to AY2024/25

Upcoming six-year cycle plan is in development per the requirements of the new General Education Model and is anticipated to be completed by August 2019.

Graduate Learning Outcomes to Be Assessed Years in which Assessment Is Planned

Population/Courses to Be Assessed

Planned Assessment Approach

Pending cycle plan development

Documents

CNM ANNUAL STUDENT LEARNING ASSESSMENT REPORT€¦ · Assessment Report Page 2 of 12 Last Revised 8/2018 PART 3: REPORT ON ASSESSMENT OF STUDENT LEARNING Assessment Method Type of