Toni Fiore's Portfolio Page
Navigation links: ETAP 623 Spring 2024 | Link to my mini-course front page
About Me
Hello, my name is Toni Fiore. I am a high school mathematics teacher working towards my CDIT degree at the University at Albany. I currently teach three different levels of Geometry at North Salem High School, ranging from Topics (applied Geometry) to Honors Geometry. I also teach a Math AIS course, where I aid students grades 8th through 9th with their mathematics skills. When I am not teaching, I coach volleyball. I coach the Varsity Girls Volleyball team at North Salem, and I coach a 16u team at Oxygen Volleyball Club in Yorktown, NY.
My Topic and Purpose
My mini-course will center around implementing Probability and Statistics into middle school and high school mathematics curriculum. This course will be targeted for educators that teach mathematics at those grade levels. In addition, this course will be beneficial for special education teachers and those who have academic support classes.
All too often, educators are faced with the difficult challenge of deciding which topics have to be simplified and sometimes skipped altogether. With only 180 days in the school year, it can feel like we do not have enough time. This is especially difficult for mathematics teachers, as there is so much that we can explore further and so much that we can implement to get the students to problem solve and to think. Probability and statistics are always the last unit in math textbooks and the least prominent in state standards. For this reason, teachers often decide to cut this unit. Out of all the different mathematics areas, for a student who will graduate and pursue a career outside of math, probability and statistics will still be useful for them to understand.
Scope of Learning Outcomes and Content
My mini-course will tackle the following key questions: Where do we see probability and statistics beyond the classroom? How will students continue to use probability and statistics after they graduate? How can we implement probability and statistics in middle school? How can we implement probability and statistics in Algebra I? How can we implement probability and statistics in Geometry?
After completing the course, mathematics educators will feel more confident implementing probability and statistics into their lessons so that students can be exposed to these topics before graduating.
Needs Assessment
My goal for this needs assessment is to determine the level of exposure that high school graduates have to probability and statistics. Based on my experience as a high school graduate and what I observe at the school I work at, I imagine that probability and statistics are topics that are of less importance to most mathematics teachers.
My purpose of this assessment is to investigate what types of courses are offered at various neighboring school districts that specifically target probability and statistics. In addition, I wish to determine if students who follow the typical pathway of Algebra I, Geometry, Algebra II, and Precalculus are exposed to probability and statistics at all.
My target population for this needs assessment is high school mathematics teachers in New York state. This is the population that would most likely benefit from my mini course, so I would like their initial feedback.
I sent out a survey to teacher contacts at six neighboring school districts on February 15 in hopes to hear back from all of them by February 24. I heard back from four out of the six, and I also filled out the survey myself on behalf of my school district. Although I did not hear back from all, the information I received was valuable. I asked the following eight questions:
1. How many students are enrolled at your school?
2. What statistics/probability courses does your school offer?
3. Would these courses count as an elective or a math credit?
4. On a scale of 1-10, how interested are your students in taking these statistics/probability courses?
5. On a scale of 1-10, how often would students who take the typical math pathway only (Algebra I, Geometry, Algebra II/Trig, Precalculus) experience exposure to probability and statistics?
6. Do you think probability is well represented in the math curriculum?
7. If you answered ‘No’ to question 6, why do you think that is?
8. Would you be interested in learning how statistics/probability can be implemented into your math curriculum?
Analysis of the Learner and Context
Of the school districts that responded, the enrollment size ranged from 400 to 1200 students. Every school offered at least one course pertaining to probability and/or statistics, but no more than two courses. Courses offered include Statistics, AP Statistics, College Statistics, Statistical Modeling and Application, Applications of Probability, and Elementary Statistics.
There was a good mix between elective courses and courses that could be used as a math credit, which can be observed in the chart below.
There was a bit of a range in student interest level to enroll in these courses, but overall, not a very high interest level.
There was a less range in student exposure to probability and statistics for students who only follow the typical pathway of taking Algebra I to Geometry to Algebra II to Precalculus.
When asked if the surveyed individuals believe probability and statistics are well represented in the typical math curriculum, all of them responded with ‘No’. When asked if the surveyed individuals would be open to learning more about how these topics can be implemented into their curriculum, three out of four of them responded with ‘Yes’.
When asked to elaborate on why they believe these areas of mathematics are so underrepresented, here were the responses.
Some patterns I noticed in the responses were lack of student interest in the courses and lack of importance placed on these courses by the schools and New York State. These responses coincide with what I notice at my school about probability and statistics. We only offer one elective course, Statistical Modeling and Application. We find that not many students want to enroll in the course, and of the students that do, it is typically students who are not very interested in pursuing mathematics in the future and took it because their counselor told them that teachers recommended them to do so. Neighboring school districts are also facing the issue that many students do not find courses like these to be interesting or hold any value for their future endeavors. Additionally, since the New York State Common Core standards place less emphasis on probability and statistics, teachers use their 180 days to focus on what is embedded in the standards.
This needs assessment and analysis leaves me with two outstanding questions that I will look to address in my mini course: How can we get students more excited about taking a probability and/or statistics course? How can we connect probability and statistics to the common core standards and make it more applicable?
Performance-Based Objectives
After completing this mini-course, learners will be able to:
- Understand the benefits of introducing probability and statistics into mathematical curriculum.
- Identify opportunities to integrate probability and statistics in algebra and geometry.
- Analyze lesson plans that implement probability and/or statistics and explain how these aspects enhanced student learning.
- Apply learning and modify an already existing lesson to include probability and/or statistics.
- Create a lesson plan that successfully ties probability and/or statistics to an existing standard in a mathematical content area of choice.
- Reflect on the implementation of the lessons created to integrate probability and statistics and seek improvement.
- Evaluate and provide feedback on classmates’ lesson plans.
Task and Content Analysis
Unit 1: Research on Relevance and Applications of Probability and Statistics
At the end of this unit, learners will be able to:
- Understand the basics of probability and statistics.
- Identify applications of probability and statistics past high school graduation.
- Identify career opportunities in probability and statistics.
- Recognize and reflect on the need for student learning in probability and statistics.
Unit 2: Implementation in Pre-Algebra I and Algebra I Topics
At the end of this unit, learners will be able to:
- Identify probability and/or statistics in Pre-Algebra I and Algebra I topics.
- Identify the connection between the application and a Common Core Standard.
- Explain how the implementation enhances student understanding of the Standard.
- Modify a lesson to implement probability and/or statistics.
Unit 3: Implementation in Geometry and Algebra II Topics
At the end of this unit, learners will be able to:
- Identify probability and/or statistics in Geometry and Algebra II topics.
- Identify the connection between the application and a Common Core Standard.
- Explain how the implementation enhances student understanding of the Standard.
- Modify a lesson to implement probability and/or statistics.
Unit 4: Applying Knowledge
At the end of this unit, learners will be able to:
- Design a lesson from scratch that ties probability and/or statistics to a mathematical topic in Pre-Algebra I, Algebra I, Geometry, or Algebra II.
- Analyze a classmate’s lesson plan and provide them with feedback.
- Reflect on the major takeaways from the course.
Curriculum Map
References and Resources
https://articles.outlier.org/jobs-for-statistics-majors
https://betterexplained.com/articles/a-brief-introduction-to-probability-statistics/
https://www.statology.org/statistics-real-life-examples/
https://www.intellspot.com/applications-of-statistics/#google_vignette
https://www.byjusfutureschool.com/blog/examples-of-probability-in-real-life/