ElemTeachPrep

=**Group 2: Elementary Mathematics Teacher Preparation**=

= Elementary Teacher Mathematics Preparation Reform =

The Elementary Math Specialist Endorsement
 * 1) Tracking the work of the EPSB Elementary Math Preparation Task Force
 * 2) Reviewing courses at KY institutions to improve the math preparation of Elementary teachers


 * 1) National standards for the elementary math specialist endorsement work group
 * 2) Kentucky standards for the elementary math specialist endorsement

Members of this group: Maggie McGatha (leader), Sara Eisenhardt, Greg Gierhart, Jonathan Thomas

=**Pertinent Research & Readings:**=

Elementary Mathematics Teacher Preparation
Mathematical Education of Teachers, Chapter 3 //Recommendations for Elementary Teacher Preparation// || ===== ===== || Mathematical Education of Teachers, Chapter 7 //The Preparation of Elementary Teachers// || ===== ===== ||
 * Conference Board of Mathematical Sciences
 * Conference Board of Mathematical Sciences
 * =====//Guidelines for Assessment & Instruction in Statistics Education (GAISE) Report// ===== || ===== [[file:GAISE Report 2007.pdf]] ===== ||
 * NCTM/NCATE Program Standards for Elementary Mathematics Specialists

CRAFTY Curriculum Foundations Project University of Michigan || ||
 * NOTE:** These standards are for initial certification programs || [[file:NCATE-NCTM Elem Standards.pdf]] ||
 * Teacher Preparation: K-12 Mathematics

Elementary Mathematics Specialists
 //Research Brief on Mathematics Specialists & Coaches // ||< ===== ===== || //Standards for Elementary Mathematics Specialists
 * < National Council of Teachers of Mathematics
 * < Association of Mathematics Teacher Educators

**NOTE:** //These standards are for advanced programs. ||< ========== || Elementary Mathematics Specialists || ||
 * Kentucky Mathematics Task Force Recommendation for
 * < Elementary Mathematics Specialists & Teacher Leaders Project

elementary mathematics specialists. State certifications, publications, and other resources are available on this site. ||< =====[|EMS & TL Project Webpage]===== ||
 * NOTE:** This webpage serves as a clearinghouse on issues related to
 * Mathematics Coaches & Specialists Resources Webpage

A bibliography of coaching literature is housed on this site. || [|Coaches & Specialists Webpage] ||
 * NOTE**: This webpage houses resources for mathematics coaches and specialists.

Numeracy Literature - What is Numeracy?

interviews. Teaching Children Mathematics, 15, 106-111. understanding of mathematical ideas. authors highlight strengths of this approach for understanding children's thinking, informing instruction, and furthering professional learning. of Nate. In M. Goos, R. Brown & K. Makar (Eds.), Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Brisbane, Vol. 1, pp. 179-186). Adelaide: MERGA. experiences often referred to as “structuring number”. use with low-attaining 3rd- and 4th-graders. This involved an intervention program of approximately thirty 25-minute lessons over 10 weeks. Focusing on the topic of structuring numbers to 20, the paper describes Nate’s pre- and post-assessments, including major gains on tests of computational fluency. Relevant instructional procedures are described in detail and it is concluded that the procedures are viable for use in intervention. Mathematical Thinking and Learning, 1, 155-177. the acquisition of formal mathematics. formal mathematics. The underlying philosophy is that formal mathematics is something that is, or should be, constituted by the students themselves. In the instructional design theory for realistic mathematics education, models always have been employed to foster a process in which formal mathematics is reinvented by the students themselves. This article describes how the use of models became more and more explicated over time and developed into the notion of emergent models. The design of an instructional sequence, which deals with flexible mental computation strategies for addition and subtraction up to 100, is taken as an instance for elaborating what is meant by emergent models and what role they play in fostering the constitution of formal mathematics. The analysis shows that there are 3 interrelated processes. First. at a more holistic level, there is a global transition in which "the model" initially emerges as a model of informal mathematical activity and then gradually develops into a model for more formal mathematical reasoning. Second, the transition from "model of" to "model for" involves the constitution of a new mathematical reality that can be denoted formal in relation to the original starting points of the students. Third, in the series of instructional activities, there is not 1 model, but the model actually is shaped as a series of signs, in which each new sign comes to signify activity with a previous sign in a chain of signification. 4) Heege, H. ter (1985). The acquisition of basic multiplication skills. //Educational Studies in Mathematics, 16//, 375-388. **NOTE:** Th e author describes the myriad strategies that children construct to negotiate multiplicative tasks. Additionally, the author discusses how support of individually constructed strategies leads to extremely rapid derivation or “knowing by heart” **ABSTRACT: ** Children learning the basic multiplications, use knowledge which they acquired in former stages. Certain additions, for instance the doubles, known by heart, can support the learning process for multiplication. It makes a great difference in cognitive achievement whether children know multiplication facts by heart or whether they are able to figure out basic multiplications. If education supports the development of informal thinking strategies, children become so skilled at this, that the border between "figuring out" and "knowing by heart" will gradually disappear. By using informal strategies children will acquire a flexible mental structure of multiplication facts instead of a collection of rules. ** PURCHASE ARTICLE **: [] 5) Kamii, C., Lewis, B. A., & Booker, B. M. (1998). Instead of teaching missing addends. //Teaching Children Mathematics,// 4, 458-461. learning experiences eliminates the need for direct instructions of arithmetic strategies. showing that if children's numerical reasoning is strong, then formal instruction of missing addends is unnecessary. Explains the findings in light of Piaget's constructivism and discusses educational implications. || rational numbers of arithmetic. The Mathematics Educator, 11, 4-9. exploration of philosophical underpinnings. J. Fischer (Eds.), Pathways to number: Children's developing numerical abilities (pp. 83-88). Hillsdale: Lawrence Erlbaum. Thompson, and others. Termed, Stages of Early Arithmetic Learning, Steffe describes a model for understanding children's conceptions of unit based upon observed arithmetic strategies. [|http://books.google.com/books?id=9emVJe9Zri0C&printsec=frontcover&dq=Pathways+to+number:+Children's+developing+numerical+abilities&source=bl&ots=5F2IGsJMmj&sig=yHcqxmQIkOUrQKpnCRZhmtmHeX0&hl=en&ei=8GWeS56LJT2NZubtIkF&sa=X&oi=book_result&ct=result&resnum=1&ved=0CAYQ6AEwAA#v=onepage&q=&f=false] || Studies in Mathematics, 26, 25-44. by Fuson. The children were selected from three classes, one a class of 5-year-olds, a second a class of 6-year-olds and from the same school, and a third also a class of 5-year-olds but from a school serving a community considered to be higher in socio-economic terms than that of the first mentioned school. Five models, one based on the theories of Steffe//et al.//, and two adapted from Fuson's study of children's elaboration of number word sequences were used to profile each child's numerical development over the school year. Significant mismatches between children's numerical development and typical curricula are described and changes to current practice recommended. Relationships between the theories of Steffe and Fuson are developed and the study's findings are compared with Young-Loveridge's study of similar focus in New Zealand.
 * 1) Ellemor-Collins, D., & Wright, R. J. (2008a). Assessing student thinking about arithmetic: Videotaped
 * NOTE ** : The authors describe the manner in which video records support assessment of students’ conceptual
 * ABSTRACT: ** Introducing an approach to detailed assessment involving videotaping clinical interviews, the
 * PURCHASE ARTICLE: [] ** ||
 * 2) Ellemor-Collins, D., & Wright, R. J. (2008b). Intervention instruction in Structuring Numbers 1 to 20: The case
 * NOTE ** : The authors lay out an instructional trajectory of collections-based (as opposed to counting based)
 * ABSTRACT: ** Nate was one of 200 participants in a research project aimed at developing pedagogical tools for
 * ARTICLE LINK: [] ** ||
 * 3) Gravemeijer, K. P. E. (1999). How emergent models may foster the constitution of formal mathematics.
 * NOTE ** : Gravemaijer describes the transitional nature of models and the manner in which this transition supports
 * ABSTRACT: **This article deals with the role that so-called emergent models can play in the process of constituting
 * PURCHASE ARTICLE : [] **
 * NOTE: ** The authors describe the manner in which attention to numerical reasoning and thoughtful design of
 * ABSTRACT: ** Presents evidence from data on how well five first-grade classes did without any formal instruction
 * 6) Olive, J. (2001). Children's number sequences: An explanation of Steffe's constructs and an extrapolation to
 * NOTE ** : Olive provides a succinct description of Steffe’s Stages of Early Arithmetic Learning along with a brief
 * ARTICLE LINK: [] ** ||
 * 7) Steffe, L. (1992). Learning stages in the construction of the number sequence. In J. Bideaud, C. Meljac, &
 * NOTE ** : Steffe describes the model built upon the extensive teaching experiments conducted by himself, Cobb,
 * PREVIEW BOOK:**
 * 8) Wright, R. J. (1994). A Study of the numerical development of five-year-olds and six-year-olds. Educational
 * NOTE ** : Wright provides a synthesis of Steffe's Stages of Early Arithmetic and a verbal sequencing model put forth
 * ABSTRACT: ** Forty-one Australian children were interviewed at the beginning, middle and end of a school year.
 * PURCHASE ARTICLE: [] ** ||