# Probability and statistics in grades 1-8

Professor Hlas |

*When we compare one thing to the other, it changes its value.*

—Gilbert

## Course Information

This course includes mathematical knowledge for teachers based on practice & content standards. Topics include:

- probability (models, compounded, conditional, expected value)
- linear functions (slope, formulas, graphing)
- statistics (sampling, measures of center, variability, normal distributions, z-scores, lines of best fit)

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

- 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.)

More course information is posted on Canvas.

### Goals

- Learn from problem solving
- Develop a productive disposition towards elementary mathematics
- Develop a growth mindset for mathematics
- Explain why mathematical ideas work

### Structure

- Daily warm-up activities, typically for discussion
- "Daily" quizzes
- One midterm examination
- Comprehensive final exam
- Extra credit via WeBWorK

### Materials

- 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.* - Calculators
**are**allowed, but are not required. Devices with wireless capabilities (e.g., cell phones) are not allowed on assessments. - Recommended review: Algebra rules

### Research background

- Common Core State Standards and CCSS Learning Progressions
- Better learning through hand writing (Science Daily, 2011)
- Nix the Tricks (Cardone)
- Improve students' learning with effective learning techniques (Dunlosky, et al., 2013, page 45)
- Benefits of study groups (Weimer, 2017)
- Examining an assessment strategy on high school mathematics achievement: Daily quizzes vs. weekly tests (Shirvani, 2009)
- Belief in learning styles may be detrimental (American Psychological Association, 2019)

## Grading

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 outside of class in a timely manner.

### Warm-up activities

Warm-up activities are intended to be completed before class and are designed to prepare preservice teachers for that day's in-class activities. These activities are more effective when everyone attends class fully prepared. "Eyeglasses" in the calendar will indicate warm-up activities.

### Book exercises

Recommended practice exercises from the book are listed in the calendar. This exercises are not graded but are recommended as these problems will likely appear on quizzes or exams.

### "Daily" quizzes (30 MP)

Most days there will be a short quiz (~10 minutes) for feedback. "Formative" quizzes will be scored in class and not graded. "Graded" quizzes will be scored by the instructor.

Notes are not allowed on quizzes. Approved calculators and manipulatives are allowed.

### Midterm (25 MP) & Final (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). A such, assessments are a part of the learning experience and will not only require mastery of class material, but will also require the ability to apply class material to new situations.

For each exam, one page of notes (1-sided, handwritten) is allowed. Approved calculators and manipulatives are also allowed.

### Online practice (+5 MP bonus)

WeBWorK problem sets are used to apply skills from class. Problems may be attempted multiple times, but feedback is limited to correct/incorrect so please contact the instructor when better feedback is needed.

Each student earns bonus points based on their percent of correct answers. For example, say a given student completes 70% of the problems. This student receives 70% of 5, or 3.5 bonus points.

### Bonus (+? MP)

Readings, quizzes, and homework may be assigned beyond those previously indicated, but final grades will still be computed based on the scale given.

#### Fine print

**Attendance** A record of attendance will be periodically collected. This is done to maintain accurate class rosters and to assess the impact of attendance on student achievement. Poor attendance may impact group activities.

If you will be absent, it is your responsibility to find out what was missed by checking D2L or contacting fellow classmates. Authorized absences (school functions or emergencies) may be made up for full credit. Assignments for non-authorized absences may be completed late for 75% credit if the assignment has not been returned to the class yet. All other make-ups receive 50% credit and must be completed within two weeks of the original due date or the last day of classes, whichever occurs first.

**Entry-level switching** The Department of Mathematics allows students within entry level mathematics courses (i.e., 010, 020, 104, 106, 108, 109, 111, 112, 113, 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.

**Midterm grades** will be based on percentage of points completed at the time of midterm submission. **Final grades** will be rounded up to the nearest whole number to determine a letter grade. Individual scores or grades will not modified because they represent a student's progress in the class throughout the semester.

**Student Accommodations** Any student who has a disability and is in need of classroom accommodations, please contact the instructor and the Services for Students with Disabilities Office in Centennial Hall 2106 to determine accommodations before contacting the instructor.

**Academic Integrity** Any academic misconduct in this course as a serious offense. The disciplinary procedures and penalties for academic misconduct are described on the UW-Eau Claire Dean of Students web site.

**Civility** As members of this class, we are members of a larger learning community where excellence is achieved through civility. Our actions affect everyone in our community. Courtesy is reciprocated and extends beyond our local setting, whether in future jobs, classes, or communities. Civility is not learned individually, it is practiced as a community.

## Other information

Catalog information: Math 303 - Probability and Statistics, grades 1-8

Meeting information:

- Section 002: Monday, Wednesday, Thursday, Friday at 12-12:50 pm
- Section 003: Monday, Wednesday, Thursday, Friday at 1-1:50 pm

Course outcomes:

- Students will be able to compute probabilities of compound situations various ways.
- Students will be able to compute expected values of a given situation.
- Students will be able to compute conditional probabilities.
- Students will be able to represent data various ways.
- Students will be able to appropriately use measures of center.
- Students will be able to appropriately use measures of variability.
- Students will be able to compare distributions.
- Students will be able to understand and interpret bivariate data.

Topical outline

- Linear functions (4 days)
- Slope: Constant rate of change
- Connections to arithmetic sequences and proportional relationships
- Linear forms: slope-intercept, point slope, standard
- Graphing linear functions

- Statistics (11 days)
- Formulating statistical questions and sampling
- Displaying single-variable data
- Measures of Center
- Measures of Dispersion
- Normal Distributions and Z-scores
- Scatter plots
- Lines of Best fit

- Probability (11 days)
- Experimental, theoretical, and simulated probability
- Tree diagrams, charts, and area models
- Game analysis
- Conditional Probability
- Expected Value

- Assessments (2 days)