# Probability and statistical thinking

Professor Hlas
hlascs (@) uwec.edu
Student drop-ins / Zoom appointments

The more I practice, the luckier I get.

## Course Information

This course focuses on mathematical knowledge for teachers using active learning.Course learning outcomes include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition of the following topics:

• probabilities of compound situations
• expected values
• conditional probabilities
• linear and non-linear equations
• representing algebraic situations
• representing data
• measures of center
• measures of variability
• comparing distributions
• understanding and interpreting bivariate data

This course helps students meet the following Liberal Education Learning Outcome(s):

• S2. Use mathematical, computational, statistical, or formal reasoning to solve problems, draw inferences, and determine the validity of stated claims.
(This outcome will be assessed by the cumulative final exam.)

### Course structure 🏗️

• First two weeks in-person. After that, Mondays/Tuesdays will use Zoom for increased engagement while Wednesdays/Thursdays will continue in-person for assessments.
• Class preparation activities for most days
• Frequent quizzes (both ungraded and graded)
• One midterm examination
• Comprehensive final exam (likely with take-home portion and in-class portion)
• Extra credit via WeBWorK homework

### Course materials 📚

1. Beckmann, S. (2014). Mathematics for Elementary Teachers with Activities, 4th edition (rental text)
I recommend printing Class Activities from Canvas so you do not need to bring the book to class.
2. Calculators are allowed, but are not required. Devices with wireless capabilities (e.g., cell phones) are not allowed on assessments.
3. Recommended review: Algebra rules

### References

#### Tips for a successful semester

The course schedule is your friend. I update this before and after class to make sure it is always as current as possible.

It is important to accurately show your mathematical thinking and to communicate clearly. On every assignment, the preservice teacher starts at zero then earns "math points" (MP) for demonstration of mathematical thinking in their solutions. If any concerns arise regarding grading, contact the instructor in a timely manner.

### Class preparation

Class preparation activities are intended to be completed to the best of your ability before class. The idea behind these activities is that you learn more by trying something first (in this case before class), then getting feedback (during class). Perfection is not expected on these activities. If tasks are unclear, please ask questions via email. Also, feel free to work with fellow classmates on these tasks.

### Extra practice

Recommended practice exercises from the book and other resources are listed in the daily calendar. These tasks are not graded but are recommended because practice problems may appear on assessments while readings provide context for class activities. Group work is recommended for extra practice problems.

### Homework via WeBWork +5 MP extra credit

Homework problem sets apply skills from class and allow for practice. Problems in WeBWorK may be attempted multiple times, but only the highest score is recorded. Feedback is immediate, but is limited to correct/incorrect so please contact the instructor when better feedback is needed.

Each student earns extra credit based on their percent of correct answers. For example, a student that completes 70% of the problems would receive 70% of 5, or 3.5 bonus points.

### Quizzes 📝30 MP

Most days there will be a short quiz at the beginning of class. Notes are not allowed on quizzes. Approved calculators and manipulatives are allowed. Quizzes will be one of the following types:

• Formative quizzes (~10 minutes) will be discussed in class and not graded. Formative assessments are sometimes referred to as assessment for learning because they designed to be part of the learning process (called the "testing effect"). After taking the quiz,I will discuss in class what I am looking for and how to score the quiz. I hope this will help you know what I consider important for grading and will also give you a method for grading your future mathematics assessments.
• Graded quizzes (~15 minutes) are a form of summative assessment because they are an assessment of learning. These will be scored by the instructor using similar procedures discussed during the formative quiz scoring. Four graded quizzes are planned, two before each exam.

### Exams 📝20 MP, 40 MP

"To assess conceptual knowledge, researchers often use novel tasks … Because children do not already know a procedure for solving the task, they must rely on their knowledge of relevant concepts to generate methods for solving the problems." (Rittle-Johnson, Seigler, Alibali, 2001, p. 347). Assessments are a part of the learning experience so will require mastery of class material and the ability to apply class material to new situations.

Exams are in-person and individually completed. Each exam focuses on more recent material, but mathematics is cumulative so expect to see previous material again. Exams allow for a note sheet (1 page, 1-sided, handwritten), approved calculators and other class manipulatives.

The final exam will include a take-home portion assigned the last week of class as well as an in-class portion. For each exam, note sheet (1 page, 1-sided, handwritten) is allowed. Approved calculators and manipulatives are also allowed. Other details will be posted to Canvas.

### Tips for a successful semester 👍

The course schedule is your friend. I continually update it to make sure it is always as current as possible. All class activities, handouts, and daily recommendations should be listed. If something is missing or unclear, please let me know so I can make improvements for the benefit of everyone in the class. Speaking of calendars, the one thing I wish I knew as a college student is to schedule study time for each class. This strategy ensures time is spent on each classes in productive ways.

Mathematics is a form of abstract thinking that is better learned through active participation. In one study (Deslauriers et al., 2019), students were either taught via lecture or through active learning. Students in the lecture class felt like they learned more, but they actually scored lower than the active learning group. Active learning means that class will often begin with a challenging problem. During class the students and the instructor will work together to solve the problem(s) and learn some mathematics along the way (Liljedahl, 2017; Brown et al., 2014; Ericsson, 2006).

One way to actively engage with mathematics is to try homework or Webwork before class discussion on the topic. This strategy helps inform your learning during class time because you will have an idea of what you know and what you still need to learn (Pan & Sana, 2021; Brown et al., 2014).

When solving problems do not expect perfection. Problems are designed to be challenging to encourage learning. Little, if anything, is learned from "easy" tasks. Speaking of learning, we will try to avoid tricks/shortcuts as these often distract us from the mathematics and create extra work to unlearn the bad habit.

After each class, educational research recommends we reflect on what was learned. One way to review is to rewrite class notes. For a specific note-taking suggestion, please see the Feyneman's Notebook Method that encourages rewriting a day's lesson with a one-page restriction. Hand-written notes also lead to more brain activity than other methods (Umejima et al., 2021; Askvik et al., 2020; ScienceDaily, 2011).

Another method for review is to focus on activities with immediate feedback. For example, WeBWorK, flash cards, study groups and practice testing all have elements of formative feedback that is immediate (Weimer, 2017; Dunlosky, 2013; ScienceDaily, 2013; Butler et al., 2008; Ericsson, 2006).

#### Frequently Asked Questions (FAQ)

When/how is the professor available outside of class?

Email is the best way to reach me. I typically respond within 24 hours, but I do not check email in the evenings or on Saturdays.

My student drop-in schedule and sign-up for Zoom appointments are posted at https://math.hlasnet.com/officehours

What is the attendance policy?

A record of attendance is required by the University to maintain accurate class rosters. Attendance is not graded but poor attendance may impact participation in group activities (e.g., taking a group quiz individually).

If you are absent, please check the course schedule then meet with the instructor via drop-in hours, Zoom, or email to make sure you are caught up. Graded work that occurs during an authorized absence (school functions, emergencies or illness) may be made up for full credit. Other absences may complete graded assignments late for 90% credit or these assignments may be completed early for full credit.

Late work is expected to be completed within two weeks of the return date or by the last day of classes, whichever occurs first. In situations where a makeup cannot occur, the final exam score may be used as a proxy for a missing assignment. Students missing a week or more of class should contact the Dean of Students Office to get extra support.

What if I am stressed out?

College can be difficult. After all, if it wasn't then you likely are not learning very much. Everyone can benefit from placing their personal well-being as a top priority throughout the semester. Should you want some emotional support for any reason, you can access free counseling services (even one short session to problem-solve solutions) from the UWEC Counseling Services on campus. They provide a variety of online and in-person services, including some virtual wellness workshops. Call them at 836-5521, stop by Old Library room 2122, or check out the website to make an appointment: https://www.uwec.edu/counseling-services/

Students also have FREE access to UW System Mental Health Support through Mantra health – a telehealth service available 24/7 days a week (call or text: 888-531-2142 or go online at: app.mantrahealth.com; sign up using your UWEC email address). You can also reach out to the WI-branch of the national crisis/emotional support text line by texting "HOPELINE" to 741 741 or use the national suicide prevention lifeline: 988 Please use these resources to support your mental well-being and success as a Blugold!

What if the math class is too easy or too difficult?

The Department of Mathematics also allows students within entry-level mathematics courses (i.e., 010, 020, 104, 109, 112, 114, or 246) to move up to a higher numbered course during the first two weeks of a semester or move down during the first three weeks. Please contact the instructor for more details or if this is not applicable.

How does grading work?

Final scores (rounded up to the nearest whole number) are compared to the grading scale given in the syllabus to determine a final grade. Individual scores or grades will not be modified because they represent a student's progress in the class throughout the semester. If there is a mistake in scoring, please contact the instructor as soon as possible to get the error fixed.

Midterm grades do not have a score table so are based on the percentage of points completed at the time of midterm submission.

Note: I dislike the University's scale of "F" because I have never once felt that a student has "failed" a class. Instead, I prefer to think of this as a "not pass" where insufficient evidence has been demonstrated by a student to move on to the next level.

What if I need accommodations (like extra time on tests)?

Please let me of know ways I might be helpful when you notice possible suggestions. For individual accommodations, please contact the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

What else do I need to know?

• Academic Integrity As described in the Blugold Student Conduct Code under student academic misconduct, "Students are responsible for the honest completion and representation of their work, for the appropriate citation of sources, and for the respect of others' academic endeavors." These student responsibilities are important, and deviations from these responsibilities have consequences. The disciplinary procedures and penalties for academic misconduct are described on the UW-Eau Claire Dean of Students web site: https://www.uwec.edu/kb/article/blugold-student-conduct-code/. If you are uncertain, please cite resources used including new technologies like OpenAI, ChatGPT, Google Bard, Snapchat AI, etc..
• Mandatory Reporter As a Wisconsin State employee, I am obligated to report any claims of sexual harassment or sexual assault. Please know that any such information revealed to me will be forwarded to the Dean of Students. The Dean of Students office may reach out to you to offer resources and support. If you wish to disclose this information to a confidential resource, you may speak to someone in the Center for Awareness of Sexual Assault, Counseling Services, or Student Health Services.
• Community As members of this class we are members of a learning community that values all people with all backgrounds. Please remember that our words and actions affect everyone within our community and also remember a little optimism can go a long way.
• See Canvas for more course information or updates.