scholarly journals A Reflective Rubric-Creating Activity that Enhances Teachers’ Mathematical Habits of Mind

2018 ◽  
Vol 6 (2) ◽  
pp. 153-171
Author(s):  
Scott A. Courtney ◽  
Judy Benjamin
Keyword(s):  
Teacher Educators ◽  
Evaluation Criteria ◽  
Career Readiness ◽  
Content Standards ◽  
Habits Of Mind ◽  
Mathematical Content ◽  
Mathematics Standards ◽  
College And Career ◽  
Practice Standards ◽  
And Mathematics

As schools and teachers in the U.S. fine-tune their implementation of mathematics standards promoting college and career readiness, the number of support resources continues to expand. One resource focus experiencing significant growth involves sample items and tasks asserting alignment with the college and career ready mathematical content and practice standards. Such samples regularly identify both the content standards addressed and the mathematical habits of mind that students have the potential to engage in. Consistently absent are evaluation criteria articulating how engagement and demonstration of associated mathematical practices can be assessed, concurrent with content. The authors discuss the development of rubrics that attempt to faithfully assess the integration of mathematical content and practice standards and highlight the benefits to mathematics teachers, coaches, professional developers, and mathematics teacher educators of engaging in such reflective rubric-creating activities.

College and Career Readiness and the Every Student Succeeds Act

2017 ◽  
Vol 53 (5) ◽  
pp. 809-838 ◽  
Author(s):  
Joel R. Malin ◽  
Debra D. Bragg ◽  
Donald G. Hackmann
Keyword(s):  
Remedial Education ◽  
Research Policy ◽  
Career Readiness ◽  
College And Career Readiness ◽  
Policy And Practice ◽  
College And Career ◽  
School Research ◽  
Education And Employment ◽  
And Mathematics ◽  
Every Student Succeeds Act

Purpose: This study addressed the current policy push to improve students’ college and career readiness (CCR) as manifested within the Every Student Succeeds Act (ESSA) and examined CCR policy in the state of Illinois as a case study, noting ways in which provisions for CCR programs prepare all students, including those historically underserved by higher education, to be prepared for education and employment post–high school. Research Methods: A critical analytic approach was undertaken, foregrounding equity. We conducted thematic content analysis of ESSA and Illinois policy, employing a CCR accountability paradigm. Findings: CCR-related content was contained throughout ESSA. Although content varied, themes were identified. Dual enrollment provisions were prominent in ESSA but not the Illinois’ CCR laws; however, science, technology, engineering, and mathematics was emphasized in both. ESSA introduced but did not fully clarify what constitutes a well-rounded education and did not identify particular reporting and accountability provisions, whereas two Illinois’ CCR bills focused on remedial education and the third evidenced a more comprehensive and integrated CCR approach. These findings suggest distinct federal and Illinois’ CCR visions. A more systematic equity focus was evident within ESSA. Implications for Research, Policy, and Practice: ESSA provisions providing new flexibilities to states portend wide variation in emphasis toward, and accountability for, long-standing equity issues. District officials will also likely have substantial flexibility in their administration, design, and implementation of ESSA-funded CCR programming, which may affect educational equity in ways that advantage and disadvantage. We thus provide several cautions and recommendations.

“A Bridge Between High School and College”

2017 ◽  
Vol 22 (1) ◽  
pp. 155-179
Author(s):  
Tonisha B. Lane ◽  
Kali Morgan ◽  
Megan M. Lopez
Keyword(s):  
Cognitive Strategies ◽  
Career Readiness ◽  
College And Career Readiness ◽  
Underserved Students ◽  
Program Administrators ◽  
College And Career ◽  
Academic Barriers ◽  
And Mathematics ◽  
Context Specific ◽  
Program Components

Underserved students express a high interest in earning a science, technology, engineering, and mathematics (STEM) degree. However, their ACT benchmark indicators tend to be much lower than their peers, especially for students who report more than one underserved attribute. There are a number of STEM intervention programs (SIPs) that are designed to retain and graduate underserved students in STEM. Yet, relatively few engage in theoretically driven, empirical research to elucidate what program components contribute to college readiness. Using Conley’s college and career readiness framework, this qualitative case study examined how one SIP helped underserved students overcome academic barriers and acquire context-specific knowledge. Findings revealed that nine interrelated practices and activities contributed to students feeling better prepared for the STEM curriculum and college expectations. Still, more attention could have been devoted to advancing key cognitive strategies. This article concludes with practical implications for SIP program administrators and faculty.

STEM Teaching and Learning via Technology-Enhanced Inquiry

2018 ◽  
pp. 595-619
Author(s):  
Michael L. Connell ◽  
Sergei Abramovich
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Career Readiness ◽  
College And Career Readiness ◽  
Pedagogical Content ◽  
Record Keeping ◽  
College And Career ◽  
And Mathematics ◽  
Stem Teaching ◽  
The Relationship

This chapter aims to address several limitations of Technological Pedagogical Content Knowledge (TPACK) – a theoretical model used in the application of technology when teaching STEM disciplines. To this end, a supplement to TPACK drawn from the Action on Objects (AO) framework (Connell, 2001) is suggested. To illustrate the value of the proposed enhancement of TPACK, an example integrating science, technology, and mathematics is provided. The Texas College and Career Readiness Standards are used to demonstrate the relationship between the proposed theoretical modification of the leading model and the current teaching practice involving such scientific activities as measuring, record keeping, analyzing, conjecturing and evaluating. Additional suggestions and applications of the TPACK/AO model are provided.

STEM Teaching and Learning via Technology-Enhanced Inquiry

2017 ◽  
pp. 221-251
Author(s):  
Michael L. Connell ◽  
Sergei Abramovich
Keyword(s):  
Teaching And Learning ◽  
Teaching Practice ◽  
Career Readiness ◽  
College And Career Readiness ◽  
Pedagogical Content ◽  
Record Keeping ◽  
College And Career ◽  
And Mathematics ◽  
Stem Teaching ◽  
The Relationship

This chapter aims to address several limitations of Technological Pedagogical Content Knowledge (TPACK) – a theoretical model used in the application of technology when teaching STEM disciplines. To this end, a supplement to TPACK drawn from the Action on Objects (AO) framework (Connell, 2001) is suggested. To illustrate the value of the proposed enhancement of TPACK, an example integrating science, technology, and mathematics is provided. The Texas College and Career Readiness Standards are used to demonstrate the relationship between the proposed theoretical modification of the leading model and the current teaching practice involving such scientific activities as measuring, record keeping, analyzing, conjecturing and evaluating. Additional suggestions and applications of the TPACK/AO model are provided.

How Do States Implement College- and Career-Readiness Standards? A Distributed Leadership Analysis of Standards-Based Reform

2018 ◽  
Vol 55 (3) ◽  
pp. 447-476 ◽  
Author(s):  
Katie Pak ◽  
Laura M. Desimone
Keyword(s):  
Distributed Leadership ◽  
Leadership Theory ◽  
Career Readiness ◽  
Content Standards ◽  
College And Career Readiness ◽  
Leadership Analysis ◽  
District Administrators ◽  
College And Career ◽  
Standards Based Reform ◽  
Theory Research

Purpose: Our primary purpose is to examine the implementation of college- and- career- readiness content standards in Kentucky, Ohio, and Texas through the lens of distributed leadership theory, and to determine the affordances and challenges of this distributed leadership through the lens of policy attribute theory. Research Methods/Approach: We analyze data from 66 hour-long interviews of state and district administrators across the three states collected from Spring 2016 to Spring 2017. Using a deductive coding approach, we developed themes around distributed leadership as they pertain to the five attributes of policy implementation: specificity, consistency, authority, power, and stability. Findings: Using the distributed leadership and policy attribute theories, we find similar trends in state leaders distributing instructional leadership to regional, district, and organizational leaders to add specificity to the college and career readiness standards at the expense of compromising the consistency and power of the reform. This distribution of leadership is thought to contribute to the authority of the reform, though this authority is made tenuous by the instability of educational policies at the national and state levels. Implications: We highlight the need to examine the implementation of education policy using leadership frameworks and to understand leadership relationships between the state their regional and district partners. We extend the use of the distributed leadership theory beyond the K-16 level and the use of policy attribute theory to showcase where state actors can strengthen their reform initiatives.

Solving Equations is All about Balance

2013 ◽  
pp. 201-214 ◽  
Author(s):  
Robin Magruder ◽  
Margaret Mohr-Schroeder
Keyword(s):  
Middle School ◽  
Conceptual Knowledge ◽  
Mathematics Classroom ◽  
Virtual Manipulatives ◽  
Content Standards ◽  
Equal Sign ◽  
Making Sense ◽  
Practice Standards ◽  
Solving Equations ◽  
And Mathematics

Virtual manipulatives provide benefits to students as they encounter the Common Core State Standards for Mathematics content and practice standards. The National Library of Virtual Manipulatives provides an abundant supply of virtual manipulatives for all K-12 grades and mathematics content areas. Specifically, in this chapter, the authors explore the use of Algebra Balance Scale manipulatives in a middle school mathematics classroom. Using virtual manipulatives increases understanding of the equal sign, algebraic symbols, and increases procedural and conceptual knowledge. In this chapter, the authors demonstrate how using virtual manipulatives helped middle school students to meet grade level content standards for solving equations in one variable. Additionally, practice standards, such as making sense of problems and persevering to solve them, modeling with mathematics, and using tools strategically through the use of virtual manipulatives are addressed. They conclude by considering practical issues related to incorporating virtual manipulatives in mathematics classrooms.

scholarly journals Comparing the Mathematical Practices Pre-Service Teachers and Mathematics Teacher Educators Identified as Relevant to Problems and Tasks

2021 ◽  
Vol 7 (3) ◽  
pp. 954-971
Author(s):  
Scott A. Courtney ◽  
Joanne Caniglia
Keyword(s):  
Teacher Preparation ◽  
Mathematics Teacher ◽  
Teacher Educators ◽  
Mathematical Practice ◽  
Teacher Preparation Programs ◽  
Habits Of Mind ◽  
Preparation Programs ◽  
Mathematical Practices ◽  
Mathematics Teacher Educators ◽  
And Mathematics

In the U.S., state adopted or developed college- and career-ready mathematics standards, including the Common Core State Standards for Mathematics, not only impact districts, students, and their teachers, but also university teacher preparation programs. In order to attain and sustain Common Core’s vision of developing mathematically competent citizens, teacher preparation programs must support pre-service teachers’ development of practical conceptions of the Standards for Mathematical Practice. In this article, we examine the mathematical practices middle grades pre-service teachers (grades 4-9 licensure) and mathematics teacher educators identified as playing a role in attempts to make sense of and work toward solutions to mathematics problems. In addition, we compare the mathematical practices indicated both within and across pre-service teachers and mathematics teacher educators. Results identify pre-service teachers’ potential difficulties operationalizing six specific mathematical habits of mind. Finally, we describe how such comparisons can guide the design of future teacher education and professional learning by describing a process for identifying problems and tasks with the greatest potential to support pre-service teachers’ development of practical conceptions of mathematics or other content-specific habits of mind.

Solving Equations is All about Balance

2013 ◽  
pp. 996-1010
Author(s):  
Robin Magruder ◽  
Margaret Mohr-Schroeder
Keyword(s):  
Middle School ◽  
Conceptual Knowledge ◽  
Mathematics Classroom ◽  
Virtual Manipulatives ◽  
Content Standards ◽  
Equal Sign ◽  
Making Sense ◽  
Practice Standards ◽  
Solving Equations ◽  
And Mathematics

Virtual manipulatives provide benefits to students as they encounter the Common Core State Standards for Mathematics content and practice standards. The National Library of Virtual Manipulatives provides an abundant supply of virtual manipulatives for all K-12 grades and mathematics content areas. Specifically, in this chapter, the authors explore the use of Algebra Balance Scale manipulatives in a middle school mathematics classroom. Using virtual manipulatives increases understanding of the equal sign, algebraic symbols, and increases procedural and conceptual knowledge. In this chapter, the authors demonstrate how using virtual manipulatives helped middle school students to meet grade level content standards for solving equations in one variable. Additionally, practice standards, such as making sense of problems and persevering to solve them, modeling with mathematics, and using tools strategically through the use of virtual manipulatives are addressed. They conclude by considering practical issues related to incorporating virtual manipulatives in mathematics classrooms.

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