Math Education Session Notes

The session starts with a collective prayer led by a participant, expressing gratitude for the opportunity to learn about math education and asking for help with studies and health for everyone involved.

Professor Kristiansen (Sharon Kristiansen) begins introductions.
- Duration at BYU: 11 years.
- Previous experience: 26 years teaching junior high mathematics.
- Courses taught: Math education courses, math courses, supervision of student teachers.

Question: What level of math did you teach?
- Subjects taught: Pre-Algebra, Algebra, Geometry, Algebra II, Secondary one and two as per the new Utah Core.
Question: Where did you teach?
- Schools: Lakeridge Junior High (14 years) and Mountain Ridge Junior High (12 years) in Alpine School District, located respectively in Orem and Highland, Utah.
Personal Question: Professor’s origin.
- Grew up in Idaho, in an area near Shelly, Goshen.

Objective: Explore sums of consecutive numbers in small groups.
- Example given: 7 + 8 = 15 (consecutive numbers).
- Other examples: 9 can be formed from 4 + 5 or 2 + 3 + 4; 22 from 4 + 5 + 6 + 7.
- Task: Find all combinations to write numbers from 1 to 15 as sums of consecutive numbers.

Organize findings in a way that facilitates pattern recognition.
Approximate time to work: 1.5 to 2 minutes.
Engage in partner discussions after individual work to examine observations and patterns.

Participants share observations and thoughts on the numbers.
Discussion on how different combinations can yield sums and the challenge of certain sums (e.g., for 2 and 8).
Notable conjectures about odd versus even numbers.
Discussion Point: Why can’t certain sums be achieved through consecutive numbers?

Observations from participants:
- Odds are easier to formulate than evens: every odd number can be achieved from sums starting from a particular set.
- Conjecture: Only certain numbers can be formed: with 2 and 4, combinations are limited.
Group discussion elicited thoughts on proving certain patterns.

Question: How did paired discussions influence individual thought processes?
- Some indicate it helped clarify misconceptions and extended thinking.

Objective: Sketch the next two figures in a given pattern provided on the worksheet.
Participants will share methods and logic in pairs regarding their sketches and findings.
Discussion about different approaches to arrive at solutions, including analytical and visual methods.

Participants explore methods for finding the total number of tiles in the 20th figure and devise a general formula.
Example formulas considered:
- General Observation: Square formulations emerge from the counting of squares and rectangles, establishing a baseline for figuring out the number of tiles in any given pattern.

Group presentations of approaches to reaching conclusions and formulating general equations, including computations with variables (n).
Understanding that while different methods may stem from the same foundational math, their representations may lead to varied outcomes.

Final reflections highlight:
- How seeing peers' work aids in personal understanding and enriches overall comprehension in mathematics.
- As a future math teacher, recognizing the myriad ways students might approach solving problems is valuable for teaching effectively.

Professor Kristiansen encourages continued exploration and learning through collaboration among students.
Expresses satisfaction with the engagement during the class and looks forward to future sessions.