The Common Core State Standards for Mathematics: What You Need to Know

Introduction 

Purpose of the study, research question(s) 

According to an alignment study between the Common Core State Standards for Mathematics and Programme for International Student Assessment (PISA), students in the United States have a weakness in executing mathematical tasks which have high cognitive demands, for instance, translating real-world situations into mathematical terms (Schleicher & Davidson, 2012). Among the Organization for Economic Co-operation and Development (OECD) countries, the US mathematics performance was below average and ranked 27 th out of 34. The purpose of this study is to, therefore, investigate the average mathematics score across the United States. 

Research Question 

What Is the mean score for the subject mathematics for both genders across the USA? 

Method(s) 

Research design (experimental, survey, etc.) 

The participants who were involved in this study were 20 high school students whose ages ranged from 14 to 18 years. They were chosen through systematic sampling where every 7 th individual was chosen to take part in the study. They were equally taken from the both genders thus constituted of 10 females and 10 male high school going students. Two of the participating students were classified as “resilient” which means that they come from a tougher background than their counterparts with different socio-economic demography. The mathematics test was designed to reinforce the students’ skills and abilities in cognitive thinking with several real-life application questions in the test. This was done with a view of enhancing necessary skills for future college success as well as their respective careers. The test was designated as web-enhanced, implying that it was posted to the course’s Blackboard website where everyone including the instructors could access the website for instructional purposes. 

Description of data collection procedures, operationalization of variables (e.g., survey questions, description of experimental procedures) 

Both students from private and public schools were sampled in this study which comprised of two stages lasting a week. After the 20 participants had been chosen systematically, an email was sent to them with the exam instructions, time and dates of the exam. Before beginning the mathematics test, a student was required to state their demographic details such as age, gender, year in school and their previous math score. 

Data analysis methods 

In analyzing the collected data, the Microsoft Excel software was utilized. The software was preferred because it provided an option to run the various descriptive statics such as measures of central tendency and variability. Furthermore, other descriptive statistics were run including frequency distribution tables and data collected represented in a histogram. 

Results 

Descriptive statistics, sample characteristics (frequency tables, range of values, means, standard deviations, etc.) 

Mathematics score
Mean	46.1
Standard Error	2.92979252
Median	47.5
Mode	32
Standard Deviation	13.10243047
Sample Variance	171.6736842
Kurtosis	-1.073672097
Skewness	0.042310999
Range	44
Minimum	26
Maximum	70
Sum	922
Count	20
Largest(1)	70
Smallest(1)	26
Confidence Level(95.0%)	6.132126219

Frequency distribution 

Raw data 

45	51	32	32	60	29	46	50	64	44
52	38	49	58	70	62	53	26	31	30

lower interval	upper interval		freq		midpoint		class boundaries
26	36		6		62		25.5	36.5
37	47		4		84		36.5	47.5
48	58		6		106		47.5	58.5
59	69		4		128		58.5	69.5
Histogram

Comparing Raw Data Distribution to “Standard” Normal Distribution using the raw data gathered in Task 2 and the sample mean and sample standard deviation calculated in Task 3 

percentage of the raw data falling within one standard deviation of the mean 

sample mean= 46.1 

sample standard deviation= 13.1024 

math scores out of 20 falls within the limits which imply 50% of the raw data falls within one standard deviation of the mean 

percentage of the raw data falling within two standard deviations of the mean 

math scores out of 20 falls within the limits which imply 100% of the raw data falls within two standard deviations of the mean 

percentage of the raw data falling within three standard deviations of the mean 

math scores out of 20 falls within the limits which imply 100% of the raw data falls within three standard deviations of the mean 

IV). Analysis and Conclusions 

From the above table obtained from excel, the mean mathematics score of the 20 sampled students was found to be 46.1% and a standard deviation of 13.1024. This means that on average the math score of a randomly selected high school student in the United States will be 46.1% or approximately 46 percent when rounded off to the nearest whole number. The standard deviation is the square root of the variance and it shows how much different math scores vary from the mean. In this case, math scores deviate by 13.1024 from the mean score. The calculated median value was found to be 47.5 and the mode which shows the most repeated score value was found to be 32. Confidence intervals are useful in determining the precision of the estimate or range of values obtained. A confidence interval is a range of values within which the population parameter may fall (Nachmias & Guerrero,2015). In this case, t he 95% confidence level value was obtained as 6.1321 . The confidence interval is given by [39.97 < 46.1 < 52.23] i.e. (46.1-6.1321 = 39.97) and ( 46.1+6.1321 = 52.23 ). This implies that the educators can be 95% confident that the mean math score of a student in the US is between 39.97 percent and 52.23 percent. Therefore, if more surveys are to be done in future, then 95% of them would result in confidence intervals that include the true population proportion. 

Taking a look at the histogram, the shape of the data of the students’ math scores can be seen. The widths are usually proportional to the classes which all the variables have been divided into and the heights of the bars are related to the class frequencies ( Donnelly, & Abdel-Raouf, 2016). The histogram of this data is symmetric in shape meaning that if it cut in the middle, the left-hand side will resemble the right-hand side. This implies that the student mathematics score dataset is from a symmetrical distribution such as the normal distribution and thus evenly distributed about the center of the data. Had the students’ math score data been unevenly distributed, the histogram would have been skewed either to the left or the right. 

This data, however, fails to follow the 68/95/99.5% "standard" normal distribution empirical rule and this is evident from the standard normal distribution performed. According to the empirical rule, 68% of the population lies within 1 standard deviation from the mean, 95% within 2 standard deviations from the mean and 99% within 3 standard deviations from the mean (Epple & Sieg, 1999). In this dataset, however, this rule did not apply since all of the sampled data lied within 2 standard deviations of the mean. The purpose of this project was to investigate the average mathematics score across the United States which has been performed and determined. The average math score was found to be 46.1% which is below average (50/100) and therefore supports the claim by Mathematics and Programme for International Student Assessment (PISA) that math performance in the United States is not very good generally. 

References

Donnelly, R., & Abdel-Raouf, F. (2016). Statistics (1st ed.). Indianapolis, Indiana: Alpha, a member of Penguin Random House LLC. 

Epple, D., & Sieg, H. (1999).  The Tiebout hypothesis and majority rule . Cambridge Mass.: National Bureau of Economic Research. 

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2015).  Social statistics for a diverse society (7th ed.). Thousand Oaks: Sage Publications. 

Schleicher, A., & Davidson, M. (2012).  Programme for International Student Assesment .  Programme for International Student Assesment . Retrieved 23 September 2017, from https://www.oecd.org/unitedstates/PISA-2012-results-US.pdf