Numbers and Operations II

Professor Hlas
hlascs (@)
Drop-in times

Fractions are pathway to algebra. (unknown)

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:

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

More course information is posted on Canvas.



Note: Calculators will not be allowed so preservice teachers can learn to think like elementary students, who do not use calculators for these mathematical topics.

Course references



It is important to clearly communicate our mathematical thinking throughout the class. 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.

"Before class" activities (0 MP)

Before class activities are intended to be completed to the best of your ability. 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 unless otherwise stated.

Formative quizzes will be take-home and are not graded. "Formative" assessments are part of learning because they provide feedback to prepare for graded/summative quizzes. Formative quizzes will be exchanged during class, then the instructor will discuss how to provide feedback to fellow students. Most days there will be a formative quiz due at the beginning of class.

"After class" activities (0 MP)

Recommended practice exercises from the book and other resources are listed in the class schedule. 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.

WeBWorK online homework (20 MP)

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 or if there is a technology issue.

WeBWorK is open until the last class day. Each student earns credit based on their percent of correct answers. For example, a student that completes 70% of the problems would receive 70% of 25, which is 17.5 MP.

Math Ed reflections (10 MP)

Reflections often involve reading(s) about education, mathematics and/or mathematics education. These assignments will be posted to Canvas and will be due throughout the semester. Scoring will vary due to the variety of prompts to address so will typically focus on how completely and clearly the prompts are addressed.

Summative quizzes (30 MP)

These will done in-class and will be graded by the instructor using similar procedures for formative quizzes. Four graded quizzes are planned, two before each exam. These may be individual, group, or hybrid (a combination of individual and group). Notes are not allowed on quizzes, but class manipulatives are allowed.

Exams (20 MP; 20 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 will require the ability to apply class material to new situations.

Two exams are planned: a midterm and a comprehensive final. Each exam focuses on more recent material, but mathematics is cumulative so expect to see previous material again. Exams are individual, allow one page of notes (one-sided, handwritten) and class manipulatives may be used. Extra credit is also planned on both exams. Other details will be posted to Canvas.

Fine print

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

Attendance/Absences 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 me (drop-in hours, Zoom, or email) so I can 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 early for full credit. Late work is expected to be completed within two weeks of the original due date or by the last day of classes, whichever occurs first. Students missing a week or more of class should contact the Dean of Students Office to get extra support.

Entry-level switching The Department of Mathematics 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.


Student Accommodations Any student who has a disability and is in need of classroom accommodations should contact the instructor and the Services for Students with Disabilities Office in Centennial Hall 2106 at the beginning of the semester.

Academic Integrity Any academic misconduct in this course will be submitted to the Dean of Students.

Mandatory Reporter As a Wisconsin State employee, the instructor is obligated to report any crimes to the Dean of Students, including claims of sexual harassment or sexual assault. The Dean of Students office may reach out to you to offer resources and support.

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 remember a little positivity can go a long way.

This class will adhere to UWEC COVID-19 policies and guidelines as found here