Classroom Interaction in Math and Science Teaching

Course Description

Classroom Interaction in Math and Science Teaching examines how teachers, students, and subject matter interact within secondary mathematics and science classrooms, and how those dynamics support student achievement. It develops reflective and practical teaching competencies for preservice teachers in grades 6–12, and includes a required field experience in secondary public schools.

Within the SCNS taxonomy, SMT is the Science and Mathematics Education prefix, and the 4000-level number places this in the upper division of a teacher preparation baccalaureate. Daytona State publishes it at 3 credits, prerequisites EDF4430, EDG4323, and TSL3080, offered spring, giving approximately 45 contact hours of instruction plus the field placement.

The three-way framing — teacher, student, and subject matter — is the course's organizing idea and it is not decorative. It is the instructional triangle, and the claim behind it is that teaching quality lives in the relationships among those three rather than in any one of them. A teacher who knows the mathematics and cannot elicit student thinking, or who manages the room well and teaches the content as procedure, is failing at the interaction rather than at a component.

Learning Outcomes

Required Outcomes

• Describe the instructional triangle and analyze classroom episodes in terms of teacher, student, and content interaction.
• Describe research on effective mathematics and science teaching at the secondary level.
• Plan lessons aligned to Florida's state standards for mathematics and science.
• Write measurable learning objectives at appropriate cognitive levels.
• Select and sequence tasks that develop conceptual understanding rather than procedure alone.
• Facilitate mathematical and scientific discourse in a whole-class setting.
• Use questioning techniques that elicit and extend student thinking.
• Apply wait time and other discourse moves deliberately.
• Elicit, interpret, and respond to student reasoning, including incorrect reasoning.
• Identify common student misconceptions in mathematics and science and address them.
• Implement inquiry-based and problem-based instruction.
• Design and manage laboratory and investigative activities safely.
• Use representations, models, and technology to support understanding.
• Apply formative assessment to inform instruction in real time.
• Design summative assessments aligned to objectives.
• Differentiate instruction for varied readiness, language, and learning needs.
• Apply strategies supporting English language learners in content classrooms.
• Apply classroom management approaches appropriate to secondary students.
• Build a classroom culture in which students are willing to be wrong publicly.
• Reflect systematically on one's own teaching using evidence.
• Complete a supervised field experience and apply course content in a real classroom.

Optional Outcomes

• Describe equity and access issues in secondary STEM participation.
• Describe interdisciplinary and STEM-integrated instruction.
• Analyze classroom video systematically.
• Describe co-teaching and inclusion models.
• Describe engineering practices in the science curriculum.
• Prepare for the Florida Teacher Certification Examinations.

Major Topics

Required Topics

• The instructional triangle
• Research on effective STEM teaching
• Florida standards and lesson alignment
• Writing objectives
• Task selection and cognitive demand
• Facilitating discourse
• Questioning and wait time
• Eliciting and interpreting student thinking
• Misconceptions in mathematics and science
• Inquiry and problem-based instruction
• Laboratory design and safety
• Representations, models, and technology
• Formative assessment
• Summative assessment design
• Differentiation
• Supporting English language learners
• Secondary classroom management
• Classroom culture and intellectual safety
• Reflective practice
• Field experience

Optional Topics

• Equity and access in STEM
• Interdisciplinary STEM integration
• Classroom video analysis
• Co-teaching and inclusion
• Engineering practices
• FTCE preparation

Resources & Tools

• 5 Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein) — short, practical, and the single most useful book on facilitating discourse. Applies directly to science as well.
• Ambitious Science Teaching (Windschitl, Thompson & Braaten) — the science counterpart, with a free companion website full of tools.
• Classroom Discussions (Chapin, O'Connor & Anderson) — the talk moves this course teaches, made concrete.
• Florida's B.E.S.T. Standards for mathematics and the state science standards (fldoe.org) — free, and what you will actually be teaching to.
• NCTM and NSTA — the professional bodies; student membership is inexpensive and both publish practitioner journals that are genuinely useful.
• Illustrative Mathematics and Achieve the Core — free, high-quality tasks and instructional materials.
• PhET Interactive Simulations (University of Colorado) — free, excellent science and mathematics simulations.
• Flinn Scientific safety resources and the NSTA safety portal — free laboratory safety guidance; see the flag below.
• FTCE test information guides (fl.nesinc.com) — free competency lists and sample items for every subject area examination.
• Desmos and GeoGebra — free, and the standard mathematics classroom technology.

Career Pathways

• Secondary mathematics teacher — grades 6–12; a persistent Florida shortage area.
• Secondary science teacher — biology, chemistry, physics, and earth-space; also a shortage area, physics especially.
• Middle grades teacher — with the appropriate certification.
• Instructional coach — districts employ mathematics and science coaches to support teachers.
• Curriculum specialist — district and state roles.
• Department chair and school leadership — the standard advancement path.
• Informal science education — museums, science centres, and Florida's substantial marine and space education sector.
• Educational publishing and edtech — content development and teacher support roles.
• Graduate study — mathematics or science education, curriculum, or educational leadership.
• SOC code 25-2031 Secondary School Teachers. Florida has ongoing shortages in mathematics and the physical sciences, which affects hiring, bonuses, and — as below — alternative certification routes.

Special Information

⚠ The task determines the thinking — and most tasks get downgraded during the lesson

The most robust finding in mathematics education research, and it applies to science equally.

Students learn what they spend time thinking about, and what they think about is determined by the task and by how it is enacted. The research finding that matters: high-cognitive-demand tasks are frequently downgraded during implementation — a task designed to require reasoning becomes a procedure because the teacher, meaning well, removes the difficulty.

The mechanisms by which it happens, all of which feel helpful in the moment:

• Telling students how to start. The struggle at the beginning of a problem is where the reasoning is.
• Breaking the task into steps so that each is manageable — which converts a problem into an exercise.
• Answering the question that was asked rather than turning it back.
• Rushing to closure because the period is ending and the class needs "the answer."
• Rewarding speed, which teaches students that mathematics is about being quick rather than about thinking.

What maintains demand instead: select tasks deliberately for the thinking they require; let productive struggle happen and be explicit with students that difficulty is expected; ask rather than tell — "what have you tried?", "why do you think that?", "does that always work?"; and sequence student solutions in the discussion so the class builds toward the idea rather than being told it.

The 5 Practices framework — anticipate, monitor, select, sequence, connect — is the concrete method for doing this, and it is worth learning properly because it makes whole-class discussion planned rather than improvised.

⚠ Wait time, questioning, and who gets to talk

Small discourse changes with disproportionately large documented effects.

• Wait time is the cheapest intervention in teaching. Classic research found teachers typically wait around a second after asking a question; extending to roughly three to five seconds produces longer student responses, more student-to-student interaction, more questions from students, and greater participation from students who rarely speak. It costs nothing and almost nobody does it, because three seconds of silence feels like a minute.
• Wait time after a student answers matters too — pausing before responding invites elaboration and signals that the answer is being considered.
• Ask more open questions. Questions with one right answer, asked rapidly, produce a lesson that looks lively and involves almost no thinking.
• Do not evaluate every answer immediately. "Interesting — does anyone see it differently?" keeps the thinking with the class; "correct!" closes it.
• Track who you call on. Participation is unevenly distributed in predictable ways, and teachers systematically underestimate the imbalance. Actually counting for a lesson is illuminating and slightly uncomfortable.
• Cold call with care and warning. Techniques such as thinking time followed by partner talk before whole-class sharing make it safe to call on anyone.
• Revoice and press. "So you're saying...?" and "how do you know?" are the workhorse talk moves.

⚠ Wrong answers are the curriculum — build a room where being wrong is safe

The classroom culture point, which is where mathematics and science teaching most often fails quietly.

• Student errors are systematic, not random. They are usually the consistent application of a rule that is almost right, which makes them diagnosable — and far more instructive than correct answers.
• Common misconceptions are documented and worth learning as content: that multiplication always makes bigger; that a longer decimal is a larger number; that the equals sign means "the answer comes next"; that heavier objects fall faster; that a force is needed to sustain motion; that the seasons are caused by distance from the sun. Each persists into adulthood and each requires deliberate confrontation rather than restatement of the correct fact.
• Telling students the right answer rarely displaces a misconception. The research on conceptual change is consistent: students need to encounter evidence that their existing model fails, and to construct the replacement.
• Intellectual safety is a precondition. If being wrong is socially costly, students will stay silent, copy, or guess — and you lose access to their thinking, which is the only thing you can actually teach with.
• Model being wrong yourself. A teacher who says "I hadn't thought of it that way — let me reconsider" teaches more about the discipline than a lecture on the scientific method.
• Watch for maths anxiety. It is documented, common, and transmissible from teacher to student — see this repository's guide to MAE2801 on the elementary version of the same problem.

The equity dimension worth naming: participation in secondary STEM is unevenly distributed, and the differences are documented by gender, race, and prior tracking rather than by ability. The teacher-level interventions that help are the ones above — task choice, discourse structures, and who gets called on — plus explicit attention to who is being positioned as competent in front of the class.

⚠ Field experience, laboratory safety, and Florida certification

Three practical matters the course sits inside.

The field experience is where the course becomes real. Treat it as an audition — districts hire people they have seen — and be useful: arrive early, ask the mentor teacher what would help, take feedback without defending, and never criticize the placement school publicly. Background screening is required, and student confidentiality obligations apply to you exactly as to staff.

Laboratory safety is a legal and professional responsibility for science teachers specifically:

• Teachers have a duty of care, and negligence in a laboratory has produced litigation and injury. Demonstrations involving flammables have caused serious student burns, and several widely used demonstrations have been formally discouraged.
• Eye protection, ventilation, chemical storage, and disposal are governed by codes and by district policy; know both.
• Safety contracts, documented safety instruction, and enforced rules are the standard of practice.
• Class size and facilities constrain what can be done safely, and a professional says so rather than proceeding.

Florida certification is administered by the Department of Education separately from your degree. The FTCE subject area examinations, General Knowledge, and Professional Education tests are required, and mathematics and science are designated shortage areas, which affects loan forgiveness eligibility, bonuses, and the availability of alternative routes. Rule 11 applies with force — Florida certification requirements, examination structures, and teacher preparation rules have changed repeatedly in recent years. Verify with the FLDOE and your programme's certification officer, not with a guide.

⚠ Only about three Florida institutions carry this number — hedge accordingly

This course appears at roughly three institutions statewide. Content, credit value, and emphasis vary more than they would for a widely taught course. Read your own institution's catalog description and syllabus rather than assuming this guide describes your section exactly, and have any transfer evaluated in writing.

How Florida course levels affect transfer

The first digit of an SCNS number denotes the year of offering, not transferability. Courses at the 1000 and 2000 levels transfer transparently between Florida public institutions, and 3000 to 4000 is unproblematic since both are upper division. The boundary that actually matters is 2000 to 3000, where lower-division credit generally cannot satisfy an upper-division requirement.

SMT4301 is 3 credits and approximately 45 contact hours of instruction plus a required field experience, offered spring. Expect applied deliverables — lesson plans, task analyses, recorded or observed teaching, video analysis, and structured reflection — rather than examination-based assessment.

SMT4301 is upper division and sits late in a teacher preparation sequence; lower-division education coursework will not substitute. Students transferring from an A.A. arrive with junior standing under Florida's articulation agreement, but teacher preparation programmes are state-approved as a whole, and completing an approved programme is the standard certification route — so confirm the pathway with a certification officer before any transfer.