Using Models to Build an Understanding of Functions

2001 ◽  
Vol 6 (5) ◽  
pp. 310-318 ◽  
Author(s):  
Kathleen Cramer
Keyword(s):  
Middle School ◽  
Elementary School ◽  
Middle School Students ◽  
Middle Grades ◽  
Early Elementary ◽  
School Students ◽  
Early Elementary School

From the time that students enter kindergarten and throughout their early elementary school years, they should have multiple experiences exploring patterns. The study of patterns for middle school students should shift to the study of functions (NCTM 1989). The question that this article addresses is how to plan and organize instruction for middle-grades students to help them develop an understanding of function.

Asked & Answered

2020 ◽  
Vol 113 (2) ◽  
pp. 164-167
Keyword(s):  
Middle School ◽  
Elementary School ◽  
Middle School Students ◽  
Systems Of Equations ◽  
School Students ◽  
Discussion Threads ◽  
Fact Fluency ◽  
Number Talks

The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to fact fluency and art-math integration in elementary school, number talks with middle school students, and classroom-tested contexts for introducing students to systems of equations.

The Importance of Equal Sign Understanding in the Middle Grades

2008 ◽  
Vol 13 (9) ◽  
pp. 514-519
Author(s):  
Eric J. Knuth ◽  
Martha W. Alibali ◽  
Shanta Hattikudur ◽  
Nicole M. McNeil ◽  
Ana C. Stephens
Keyword(s):  
Elementary School ◽  
Middle Grades ◽  
School Education ◽  
School Mathematics ◽  
Instructional Time ◽  
Early Elementary ◽  
Equal Sign ◽  
Grade Levels ◽  
Elementary School Education ◽  
Early Elementary School

The equal sign is perhaps the most prevalent symbol in school mathematics, and developing an understanding of it has typically been considered mathematically straightforward. In fact, after its initial introduction during students' early elementary school education, little, if any, instructional time is explicitly spent on the concept in the later grades. Yet research suggests that many students at all grade levels have not developed adequate understandings of the meaning of the equal sign (Baroody and Ginsburg 1983; Behr, Erlwanger, and Nichols 1980; Falkner, Levi, and Carpenter 1999; Kieran 1981; Knuth et al. 2006). Such findings are troubling with respect to students' preparation for algebra, especially given Carpenter, Franke, and Levi's (2003) contention that a “limited conception of what the equal sign means is one of the major stumbling blocks in learning algebra. Virtually all manipulations on equations require understanding that the equal sign represents a relation” (p. 22).

scholarly journals Teaching Evolution Concepts to Early Elementary School Students

2009 ◽  
Vol 2 (3) ◽  
pp. 458-473 ◽  
Author(s):  
Louis Nadelson ◽  
Rex Culp ◽  
Suzan Bunn ◽  
Ryan Burkhart ◽  
Robert Shetlar ◽  
...  
Keyword(s):  
Elementary School ◽  
Elementary School Students ◽  
Early Elementary ◽  
School Students ◽  
Teaching Evolution ◽  
Early Elementary School

scholarly journals Virtual Manipulatives: A Tool to Support Access and Achievement With Middle School Students With Disabilities

2019 ◽  
Vol 35 (1) ◽  
pp. 51-59 ◽  
Author(s):  
Emily C. Bouck ◽  
Leslie A. Mathews ◽  
Corey Peltier
Keyword(s):  
Middle School ◽  
Middle School Students ◽  
Students With Disabilities ◽  
Middle Grades ◽  
Virtual Manipulatives ◽  
School Students ◽  
Content Areas ◽  
Mathematical Content ◽  
Concrete Manipulatives ◽  
Instructional Needs

Manipulatives offer students with disabilities access and support in classrooms. However, it is important for educators to be aware that concrete manipulatives are not the only option. Teachers serving students identified with a disability in the middle grades may consider selecting virtual manipulatives as supplement, complement, or in lieu of concrete manipulatives. In this technology in action, the authors provide information for educators about using virtual manipulatives and how they can be used across different settings, instructional needs, and mathematical content areas for middle school students with disabilities.

An Interprofessional Approach to Dialect-Shifting Instruction for Early Elementary School Students

2021 ◽  
Vol 52 (1) ◽  
pp. 139-148 ◽  
Author(s):  
Arynn S. Byrd ◽  
Jennifer A. Brown
Keyword(s):  
Elementary School ◽  
Student Satisfaction ◽  
Elementary School Students ◽  
American English ◽  
Third Grade ◽  
Early Elementary ◽  
School Students ◽  
Third Grade Students ◽  
Early Elementary School ◽  
Grade Level Differences

Purpose Dialect-shifting has shown promise as an effective way to improve academic outcomes of students who speak nonmainstream dialects such as African American English (AAE); however, limited studies have examined the impacts of an interprofessional approach with multiple instructional methods. In this study, we developed a dialect-shifting curriculum for early elementary school students who speak AAE and evaluated the curriculum for feasibility and preliminary impacts. Method Forty-one kindergarten, first-, second-, and third-grade students and their teachers in one elementary school participated in a 7-week dialect-shifting instruction co-taught by the classroom teachers and a speech-language pathology graduate clinician. Students' use of dialect-shifting and dialect density was measured by calculating dialect density measures in retells presented in AAE and mainstream American English and responses to situational dialect-shifting and applied dialect-shifting tasks. Teacher surveys and interviews about the feasibility and perceived impacts were conducted. Results Initial impacts of the curriculum demonstrated increased dialect awareness for all students, with grade-level differences when students were asked to explicitly dialect-shift. In particular, second- and third-grade students were more proficient at dialect-shifting AAE features included in the curriculum. Additionally, high rates of administrator, teacher, and student satisfaction, teacher generalization, and maintenance of incorporating contrastive analysis instruction into class activities were reported. Conclusions Literacy and play-based instruction are feasible methods to create a dialect-shifting curriculum tailored to younger students. Furthermore, the feasibility and effectiveness of the curriculum were supported by an interprofessional approach. Supplemental Material https://doi.org/10.23641/asha.13524317

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