Teaching Elementary Mathematics

Instructor Information

• Instructor: Dr. Carmen Montoya (Assistant Professor of Teacher Education)
• Email: cmontoya@university.alkimi.ai
• Office: Lovell Hall 128
• Office Hours:
  • Wednesday & Friday: 1:30–3:00 p.m. (In person, Lovell Hall 128)
  • Tuesday: 11:00 a.m.–12:00 p.m. (Virtual via Zoom; link posted in Canvas)
  • Also available by appointment.

Course Description

Number sense, operations, fractions, geometry, and measurement for grades K–6, with standards-based planning, manipulatives, and student-thinking-centered instruction. EDUC 315 prepares elementary teacher candidates to design and implement standards-based, student-centered mathematics instruction across kindergarten through grade 6. Grounded in the National Council of Teachers of Mathematics (NCTM) Process Standards and state mathematical content domains, candidates investigate early number sense, place value, operations, rational numbers, algebraic thinking, geometry, and measurement. Candidates learn to employ the Concrete-Representational-Abstract (CRA) instructional sequence, utilize physical and digital manipulatives, lead number talks, analyze student misconceptions, and support multilingual learners in developing mathematical discourse.

Prerequisites

Admission to Teacher Education and MATH 105.

Measurable Student Learning Outcomes

Upon successful completion of EDUC 315, students will be able to:

1. Analyze Mathematical Trajectories in Grades K–6: Examine learning progressions and standards-based trajectories across early numeracy, whole number computation, fractions, decimals, algebraic reasoning, and geometry.
2. Implement the Concrete-Representational-Abstract (CRA) Model: Design mathematics lessons that sequentially bridge concrete manipulatives (e.g., base-ten blocks, fraction strips), visual representations, and abstract symbolic notation.
3. Conduct Diagnostic Clinical Math Interviews: Administer an individualized clinical interview to assess an elementary learner's conceptual understanding, diagnosing misconceptions and identifying next instructional steps.
4. Facilitate Meaningful Mathematical Discourse: Plan and execute inquiry-based number talks, choral counting, and three-act math tasks that promote math talk, argumentation, and access for bilingual/multilingual learners.
5. Design a Standards-Based Elementary Mathematics Unit Plan: Develop a multi-day, differentiated elementary mathematics unit plan featuring formative checks, rich problem-solving tasks, and Universal Design for Learning adaptations.

Required Course Materials & Approximate Costs

1. Van de Walle, John A., Karen S. Karp, and Jennifer M. Bay-Williams. Elementary and Middle School Mathematics: Teaching Developmentally. 10th ed., Pearson, 2019. Approx. $95 print, $50 digital rental.
2. National Council of Teachers of Mathematics. Principles to Actions: Ensuring Mathematical Success for All. NCTM, 2014. Approx. $35 print or digital.
3. Total estimated cost: $85 to $130.

Generative AI Policy (AI Level 2: AI Permitted with Disclosure for Specified Tasks)

In accordance with Alkimi University Academic Policies (Student Handbook §5.8), EDUC 315 operates under AI Level 2.

• What is permitted: You may use generative AI tools to brainstorm real-world contexts for elementary word problems, generate variations of mathematical tasks, and proofread draft lesson plan descriptions for grammatical correctness.
• What is prohibited: You may not use generative AI to diagnose student mathematical misconceptions in clinical interview assignments, write your comprehensive elementary math unit plan, or complete weekly methodology quizzes. The analysis of student mathematical reasoning must be your own work.
• Disclosure: All submitted lesson plans, microteaching reflections, and unit portfolios must include an AI disclosure statement stating which generative AI tools were consulted and how their suggestions were revised or integrated. If no AI tools were used, state: 'No generative AI tools were used in preparing this work.'

Grading Components and Weights

• Midterm Examination 1: 15% (In class, Thursday, October 1)
• Midterm Examination 2: 15% (In class, Thursday, November 12)
• Student Mathematical Thinking & Clinical Interview Analysis: 20% (Due Friday, October 23 at 11:59 p.m.)
• Number Talk Design & Microteaching Simulation: 15% (Due Friday, November 20 at 11:59 p.m.)
• Weekly Math Methods & Manipulative Canvas Quizzes: 15% (Due Mondays at 11:59 p.m. in Canvas; lowest quiz score dropped)
• Comprehensive Elementary Mathematics Unit Plan & Portfolio: 20% (Due by the end of the final exam period, Thursday, December 17, 2026, 3:30–5:30 p.m.)

Grading Scale (Alkimi University Standard)

• A: 93–100% | A-: 90–92%
• B+: 87–89% | B: 83–86% | B-: 80–82%
• C+: 77–79% | C: 73–76% | C-: 70–72%
• D+: 67–69% | D: 60–66% | F: Below 60%
• Extra credit: No individual extra credit assignments are offered in this course.

Course Schedule (Fall 2026)

Course Policies

Attendance Policy

Class attendance and hands-on participation in manipulative workshops and microteaching simulations are essential. Elementary math methods relies upon cooperative peer problem solving and experiential modeling of mathematical concepts. If illness or an emergency prevents attendance, notify Dr. Montoya prior to class. More than two unexcused absences will result in a deduction from your course grade. Students who miss the first two class meetings without notifying the instructor may be dropped. Students may miss class for religious observance without penalty if they notify the instructor in writing within the first two weeks of the semester (by Wednesday, September 9, 2026). Absences for university-sponsored activities (athletics, performances, conferences) are excused with a letter from the sponsoring office at least one week in advance.

Late Work Policy

Assignments submitted after the deadline will lose 10% per calendar day for up to 72 hours. Submissions beyond three days late will not be accepted. Weekly Canvas quizzes must be completed before the posted Monday deadline.

Teacher Education Admission Prerequisite

Enrollment in EDUC 315 requires formal Admission to Teacher Education (including at least 45 earned credits, 2.750 GPA, basic skills exam, and background check) and completion of MATH 105. Teacher candidates must achieve a grade of C+ or higher to progress toward clinical student teaching.

Final Exam Policy

EDUC 315 has no final examination. The comprehensive elementary mathematics unit plan & portfolio takes its place. Nothing is due on Reading Day (Thursday, December 10, 2026).