The area of statistics has been receiving more attention over the past few years. Many degree programs at colleges require students to take courses in statistics. For example, in addition to the normal math and science fields that would require it, business degrees are requiring students to have a greater understanding of statistics by successfully completing at least one course in statistics. Secondary institutions must step up and ensure that students can go on to be successful in a college statistics course. Only a few years go the College Board added Advanced Placement Statistics. The purpose of this paper is to examine if after completing Algebra I and Algebra II students have been adequately prepared to be successful in AP Statistics and later on in other college statistics courses. In order to accomplish this I will be critically examining the General Level Expectations for 9th through 11th grade.
In order to be adequately prepared for AP Statistics it is imperative that students be exposed to the concepts of: data collection, data analysis, probability, graphical representation of data, graphing calculators and computer software. The AP Statistics syllabus does not allow time to teach these ideas from scratch. Instead, a teacher should simply build on the foundations of these concepts in order to have a successful AP Statistics course. AP Statistics is a portfolio assessment class by nature thus much of the class time is devoted to students completing projects that force them to apply what they have learned. This is the main reason that there is not much room in the syllabus to revisit the basics of the concepts mentioned above.
Data collection is addressed in the 11th 12th grade GLEs. GLE D-1-F states “Discuss the differences between samples and populations and devise and conduct well-designed experiments/surveys involving randomization and considering the effects of sample size and bias.” This GLE addresses the basics of data collection: choosing whom to collect data from. The AP Statistics syllabus requires students to complete a study. This GLE lays a great foundation for an AP Statistics teacher to build upon.
Data analysis is addressed in GLE D-8-H which states, “Draw and justify conclusions based on the use of logic (e.g., conditional statements, converse, inverse, contra positive).”Furthermore in GLE D-2-H “Show or justify the correlation (match) between a linear or non-linear data set and a graph ” Finally GLE D-1-H “Determine the most appropriate measure of central tendency for a set of data based on its distribution and identify trends in data and support conclusions by using distribution characteristics such as patterns, clusters, and outliers.” These GLEs were found in the 9th and 10th grade divisions. Students should be able to begin basic analysis of a data set to determine if there is a correlation, if it is linear or nonlinear, and identify trends in the data set that can be supported. These are very simple forms of data analysis however it is imperative that students be equipped with these going into AP Statistics. In order to learn t-tests and more advanced data analysis techniques students must have the basics.
Probability is a key concept that students must understand before taking a course in statistics. GLE D-4-H addresses probability in 9th grade, “Define probability in terms of sample spaces, outcomes, and events; compute probabilities using geometric models and basic counting techniques such as combinations and permutations; and explain the relationship between the probability of an event occurring, and the odds of an event occurring and compute one given the other.” These give a firm understand of what probability is. Furthermore, students should be able to compute probabilities and explain relationships. The most important part of this GLE is that students be able to explain relationships. In AP Statistics it will be important to discriminate the relationships between probabilities. Especially when completing a study. Students will have to discuss their findings, which is a hard concept to grasp. However, if they have the basics of talking about relationships then it will be much easier to understand how to write a discussion on a given set of data.
It is imperative that students be familiar with simple graphical representations of data prior to taking AP Statistics. Students not only need to be able to graphical represent data but be able to interpret and analyze a graph or chart of data. GLE D-7-H addresses this concern. It states that students should be able to understand and create data in the form of a table, bar graph, line graph, scatter plot, matrix or circle graph. This should be accomplished by the end of the 10th grade. There are too many forms of graphical representation of data to cram into one statistics course. Thus, students need the basics prior to AP Statistics because the curriculum for AP Statistics does not allow time for covering the basic forms of graphical representation.
Students are expected to enter an AP Statistics course with a strong ability to operate a graphing calculator. The basics of graphing and entering equations is not covered in the AP Statistics curriculum and takes entirely too long to teach if students are not already familiar with the graphing calculator. The 11th 12th grade GLEs address technology in D-2-H “interpret and explain, with the use of technology, the regression coefficient and the correlation coefficient for a set of data.” Technology can mean a wide variety of things, however, a graphing calculator is easily used to deal with regression. Sadly, this is the only GLE that addresses the use of technology for analysis of a data set graphing calculator or otherwise.
It is important to note that just because a GLE exists doesn’t mean that it is followed or accomplished in the course of a year. There are many other factors such as: teacher content knowledge, teacher priorities, curriculum and time constraints. It would be unreasonable to assume that every student entering AP Statistics would have all of the mentioned foundations.
Teachers may not have the content knowledge to teach statistics concepts. When I was in school statistics were not emphasized in the curriculum. Teachers who haven’t been to professional development classes might not want to do a lot with the statistics concepts because they do not feel comfortable with the concepts. Unfortunately this does happen. For instance, I have spoken with teachers who don’t teach word problems because they have trouble solving them and don’t want to seem like they don’t know what they are talking about.
In addition, there is so much to cram into one year that time often becomes an issue. Teachers have to ask themselves what is the most important thing to teach. Unfortunately, in my opinion most teachers don’t heavily weight concepts that are related to statistics. However, students need just as much of a background in statistics as they do in other algebra concepts. Especially in today’s world where employers and colleges are demanding that people know more about statistics.
Curriculum is another issue. My textbook from last year when I taught Algebra I was the Louisiana edition. It was supposed to follow the GLEs created for the state of Louisiana. However, there was not a section that covered scatter plots, bar graphs, tables or circle graphs. In addition, I as a teacher didn’t know that it was supposed to be taught. I was told from administration that the text included all the state GLEs when in fact it barely mentioned graphical representation of data. Curriculum needs to be investigated to ensure that it is adequately covering statistics topics.
There are several recommendations that I would make to ensure that students are adequately prepared for an AP Statistics class. First, the GLEs have set a great foundation, however, some of them need to be moved to earlier years. AP Statistics can be taken in either the junior or the senior year in high school as long as Algebra I and Algebra II have been completed. It is necessary to ensure that students have the knowledge prior to taking the course.
In addition, professional development is key. Teachers need to be educated on the importance of statistics in today’s world. Workshops need to be created at an affordable price that teachers can attend to help teach statistical concepts and to explain that it is important. Perhaps even implementing a professional development within all public schools during in-service. Furthermore, the professional development would need to include instruction on how to operate graphing calculators a computer modeling software. Using computers to do mathematics is a fairly new concept and many teachers do not understand the technology and therefore don’t use it in the classroom. At my school, I am the only math teacher that knows how to use a graphing calculator therefore students don’t learn how to use a graphing calculator until they are in my Advanced Math or AP Calculus course.
The state has set the stage for students to succeed in an AP Statistics course. However, there are a few changes that need to be made to improve the system. For instance, teachers need to be educated about the latest trends in technology and in the importance of statistics. Teachers also need to be educated with statistics content knowledge where necessary. In addition, some of the GLEs need to be accomplished prior to the 11th grade year to ensure that students have all the necessary foundations. Lastly, curriculum needs to be evaluated to ensure that it does give enough attention to statistical concepts.