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Possible Title:

Effect on mathematics instruction involving rate of change or slope before and after professional development on content and rich task creation.

Research Question :

What is the level of teacher knowledge on various representations of slope? (Content Assessment) Before and after immersion in content over summer professional development.

What are the characteristics of a lesson or unit of study where slope or rate of change is included as perceived by teachers prior to professional development? (Each teacher will bring a copy of a lesson or unit that includes rate of change/slope; Interview)

What are the characteristics of a lesson or unit of study where slope or rate of change is included as perceived by teachers after initial professional development is completed? (Teacher’s will develop a unit of study where rate of change/slope is included; Interview after initial professional development and after facilitation of the unit.)

What are teacher’s views on rich task creation of lesson(s) on rate of change/slope?

INSTRUMENTS FOR ADMINISTRATORS AND TEACHERS
Content Assessment

STRUCTURED ABSTRACT
Background:

Purpose:

Setting:

Subjects:

Research Design:

Data Collection and Analysis:

Findings: To be determined

Conclusion: To be determined

DEFINITIONS

BELIEFS: When provided with evidence beliefs can change (Cooney, Shealy, & Arvold, ____)

Phillip (2007) lenses through which individuals interpret their surroundings. Thompson (1992) as referred to in Trujillo states that beliefs can be influenced by what a person experiences, they can be flexible.

CONCEPTIONS: “Mental structure encompassing beliefs, meanings, concepts, propositions, rules, mental images, preferences, and the like (Thompson, 1992, p. 130 as given in Trujillo)

CONSTRUCTIVIST THEORY: Conjectures, proofs, and refutations that together is a social construct that is subject to change and judged according to the culture (Thompson, 1992).

EQUITY PRINCIPLE: “All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study and support to learn mathematics” (NCTM, 2000, p. 12).

LEADERSHIP CONTENT KNOWLEDGE: Administrators views on teaching and learning mathematics, being able to recognize and encourage best practices in the classroom and knowledge to set expectations of math teachers (Stein & Nelson, 2003). Need to be able to monitor and promote NCTM Process Standards (Trujillo, 2010). Knowledge of the subject, beliefs regarding teaching and learning the subject (Goldsmith & Nelson, 2006).

OPPORTUNITY TO LEARN:

PEDAGOGICAL CONTENT KNOWLEDGE: “The blending of content and pedagogy into an understanding of how particular topics, problems, or issues are organized, represented, and adapted to the diverse interests and abilities of learners, and presented for instruction” (Shulman, 1987, p. 8).

PRIME LEADERSHIP PRINCIPLE OF EQUITY:

PROBLEM SOLVING APPROACH: Reasoning, gathering and organizing data needed to answer the question, communicating ideas and results, reflecting on the approach and the result, and cycling through the procedure as many times as needed (Thompson, 1992).

PROFESSIONAL LEARNING COMMUNITY:

REFORM INFRASTRUCTURE: The environment needed to support improvement efforts that are school wide (St. John, et al., 1999).

REFORM MATHEMATICS: Pedagogy that begins and focuses on the learners mathematical conceptions and misconceptions (Ball & Cohen, 1999) as given in Trujillo (2010). Based on the constructivist theory where the learner is engaged in “doing” mathematics.

SENSE-MAKING: Helps admin make connections between beliefs and policy (Trujillo, 2010)

SOCIAL CONSTRUCTIVISM: every individual constructs their own knowledge according to their environment (Trujillo, 2010).