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**MAE 605 Case Study Solutions on Quantitative Research Methods in Mathematics Education**

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**CASE ONE**

After interacting with a 400 level Mathematics Education student, Mr Stephen Atepor realized that the student in question never read Elective Mathematics at the Senior High School level. The student explained that she actually developed interest in Mathematics at the College of Education. After graduating from college, she taught mathematics at the Junior High school level for some years and later got admission to the University to pursue Bachelor of Education in Mathematics Education. Although the University’s policy indicates that Elective Mathematics was a pre-requisite for Bachelor of Education in Mathematics Education, this very student seem to have defied the assertion that “Students without Elective Mathematics were not qualified to study Mathematics Education”.

After probing for a while, Mr Atepor got to know that few students had read the same program successfully in the past and from other universities. Mr Atepor spotted a potential research area. He didn’t know how to identify such students or past students, but was assured by the pre-service teacher that she could link him up to one other colleague of hers. After some weeks, Mr Atepor had reached seven people who had agreed to willingly participate in the research. He therefore sought to investigate the mathematics learning experiences of students who were either pursuing or had pursued their first or first two degrees in Mathematics Education without necessarily having Elective Mathematics Background at the secondary school level.

- Is the study qualitative or quantitative?
- Justify your position in (a) above
- State and justify the appropriate sampling technique used in the study
- Is the sampling technique stated in (c) above probability or non-probability?
- Suggest a possible research topic for the study above
- What possible data collection instrument is Mr Atepor likely to use?
- Describe a possible way by which the data collected by Mr Atepor could be analyzed

**CASE TWO**

In a study to investigate the effect of teaching circle theorem with autograph software on the achievement of SHS 2 students in Senior High schools, two classes from two different schools were used: class E (with 18 females and 15 males) was the experimental group while class C (with 20 females and 23 males) was the control group. Both classes were made to take a test whose scores were collated and labeled TEST 1. The E group was taught circle theorem using the autograph software while the C group was taught using the conventional method. After the three-week lessons, the students in both groups were tested again. The test scores were labeled TEST 2. The test scores were analyzed using appropriate statistical tools. Conclusions and inferences were made accordingly. Answer the following questions:

- Is the study adopting qualitative, quantitative or mixed methods approach? Explain your answer
- Could the two groups (E and C) be selected from the same school? Provide justifications for your stance
- What is the sample size in the study?
- What name, in such a research, can be used for TEST 1 and TEST 2 respectively?
- What was the data collection instrument used in the study?
- What two practical measures could be taken to ensure external validity?
- What two practical measures could be taken to ensure internal validity?
- What statistical tool is appropriate to compare the achievement levels between the E and C groups?
- If the researcher wants to cater for any possible extraneous variable, what statistical tool would be the most appropriate to use in comparing the performances of the students in the E and C groups?
- List two assumptions required to use the statistical tool in (h) or (i) above

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