Numbers and Operations II

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

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):

Course structure 🏗️

Course materials 📚

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 🔍

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.

Grading

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.

More information & practice 📖🖋️ 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 and readings provide context for class activities. Group work is recommended for extra practice problems.

WeBWorK 10 MP 2 MP bonus

WeBWorK is an online homework system with problem sets that apply skills from class and allow for practice. Problems in WeBWorK may be attempted multiple times and 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 points based on their percent of correct answers completed on time. So a student that completes 25% of WeBWorK gets 2.5/10 MP, completing 50% gets 5/10 MP, and completing 100% scores 10/10 MP.

Math Ed reflections 💭 15 MP

Reflection assignments provide additional context for how our class connects to other aspects of mathematics education. Scoring will vary due to the variety of prompts to address so will typically focus on how completely and clearly the prompts are addressed.

Five math ed reflections are planned: an introduction, two readings, and two exam preparations.

Quizzes 🤔 25 MP

Quizzes may be formative or summative. Formative quizzes done as part of learning. These quizzes are not graded, but will be exchanged during class so other students can see different solutions to the same problems. The instructor will highlight important aspects of solutions so preservice teachers can practice giving feedback.

Summative quizzes will be graded by the instructor using similar procedures for formative quizzes. Typically these will be hybrid (a combination of group and individual), but may be all group or all individual depending on the content. Notes are not allowed on summative quizzes, but class manipulatives are allowed.

Four summative quizzes are planned, two before each exam.

Exams 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.

Two exams are planned, a midterm about halfway through the semester and a final exam.

Exam bonus +10% MP

The highest exam score (including the final exam) will be given +10% MP bonus to allow for individual differences between students. This will be computed at the end of the semester.

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 bad habits.

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 due 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 for other solutions.

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 that 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?