Standards For Mathematical Practice Research Articles

The Critical Roles of a Mathematics Specialist in Establishing Effective, Coordinated Professional Development Systems

ABSTRACT For nearly three decades, mathematics research has indicated the need for high-quality mathematics instruction including both ambitious and equitable practices, as well as continuous, innovative learning opportunities for educators. Teaching practices and standards for mathematical practice have been identified to provide guidance. While research connects effective professional development (PD) to improved instructional practices, there is a need for additional research on the role mathematics specialists play in developing and sustaining PDs. This qualitative case study examined the multiple roles of a specialist while laying the foundational components for a coordinated PD system to improve and strengthen mathematics teaching and learning in elementary classrooms. The PD efforts included the implementation of a teacher subsystem where a specialist led all components consisting of pull-out PD, mathematics coaching, collaborative time, and teacher networks. This study took place at a rural, pre-K through fourth-grade school in a southeastern state. Analysis of the data identified the specialist’s key roles in each component of the teacher subsystem. The results indicated that the development and implementation of a teacher subsystem impacts the overall effectiveness of PD. Findings serve as a foundation for specialists to design and implement coordinated efforts that can have positive impacts on the teaching and learning of mathematics.

Using Fermi Questions to Foster Community

Two teachers describe how to use Fermi Questions to illuminate the connections between the Standards for Mathematical Practice and the social and emotional learning competencies.

Symbiosis: Social and Emotional Learning & Mathematics Learning

Social and Emotional Learning and the Standards for Mathematical Practice have a mutually beneficial relationship and develop mathematically proficient and confident students.

Integrated STEM as Problem-Solving Practices

ABSTRACT Mathematics is foundational to integrated science, technology, engineering, and mathematics (STEM) education. Problem solving is central to integrated STEM and to the individual disciplines as evidenced by the practice standards of each discipline (e.g., Standards for Mathematical Practice, Science and Engineering Practices, and Technology and Engineering Practices). We situate integrated STEM as problem-solving practices by synthesizing practice standards from each discipline into four integrated STEM practices: (1) use critical and creative thinking to define and solve problems, (2) collaborate and use appropriate tools to engage in iterative problem solving, (3) communicate solutions to problems based on evidence and data, and (4) recognize and use structures in real-world systems. The integrated STEM practices are critical components of high-quality STEM learning experiences that allow students to apply discipline specific content to authentic problems. When each and every student is provided access and opportunity to high-quality integrated STEM learning experiences, they understand how mathematics is used in the real world and have more favorable views of mathematics. Mathematics education research could use the integrated STEM practices to rigorously investigate calls for greater access, equity, and opportunities in teaching and learning mathematics in integrated STEM contexts.

Picturebook Biography Read‐Alouds and Standards for Mathematical Practice

AbstractRead‐alouds of picturebook biographies offer children engaging windows into the lives and work of famous (and sometimes not‐so‐famous) mathematicians to observe and discuss their ways of learning and doing mathematics—their mathematical practices. The Standards for Mathematical Practice (SMPs), although generally embodied in the work of successful mathematicians throughout the ages, were only recently identified and prescribed for US mathematics curricula. The authors provide a rationale for using the context of story to introduce the SMPs to elementary students and share picturebook Read‐Aloud Lesson Ideas as samples for inviting discussions about selected Standards. Three figures list additional biographies in the categories of Computer Science and Coding, Space Exploration, and Other Related Mathematics Fields and provide an analysis of two selected SMPs for each book.

Embracing Common Core Standards for Mathematical in Secondary Mathematical Practice

Teachers' support in implementing the standards for mathematical practice has been an area of study since the implementation of the Common Core state standards initiative. The research problem had a gap in the literature regarding what teachers perceive as the supports needed to implement the Common Core standards for mathematical practice in the classroom. The Common Core initiative's standardized educational reform goal is to better prepare students for career and college readiness in the United States. Fidelity in implementation is essential to the success of the reform. The purpose of this qualitative research was to explore what teachers perceive as the supports needed to implement the Common Core standards for mathematical practice in the classroom. Twelve middle school mathematics teachers participated in semistructured interviews to provide data on their use of the standards and their perception of support needs. The conceptual framework of this study was the interconnected model of professional growth. The results of the study indicated a reported gap in practice regarding the use of the standards from the teachers’ account. They further identified the need for formal training to understand better and use the standards. The support teachers seek is to have training that can allow them to learn more about the purpose of the standards and training that can be adapted to their needs based on their current practices and experiences. The research findings can help with the fidelity of implementation, and possibly influence social change by assisting teachers in using best practices to prepare students for college and career readiness in mathematics. Keywords: Common core, college readiness, fidelity, mathematics instruction, college career readiness DOI: 10.7176/JEP/12-8-02 Publication date: March 31 st 2021

Data Saves the Whales!

Data Saves the Whales! was developed as part of the Advanced Manufacturing and Prototyping Integrated to Unlock Potential (AMP-IT-UP) project, funded by the National Science Foundation through its Math and Science Partnership program. A central outcome of the AMP-IT-UP project was the development of 1-week modules for core middle school math and science courses that were aligned with best practices as put forth in the Next Generation Science Standards and Standards of Mathematical Practice. Data Saves the Whales! is a middle school mathematics module that is set within a marine ecosystem. It focuses on independent and dependent variables and Cartesian coordinate graphing, and on math practices related to data representation—i.e. how data can be represented in different ways to communicate various messages to an audience. Students engage in a simulated investigation to collect oceanographic data, meant to mimic the experimental procedures used by marine scientists when collecting samples, and learn different methods of graphing the data to effectively communicate their findings. This module features work conducted by the research team of Dr. Ellery Ingall, Professor of Earth and Atmospheric Science at Georgia Tech, and integrates math skills with marine science and the concepts of food webs and the interdependence of organisms.

Documenting increased participation of a student with autism in the standards for mathematical practice.

The Common Core State Standards articulate expectations for student participation in mathematical reasoning, sense making, and discussion. Yet little to no research explores the participation of students with autism in these practices. Drawing on neurodiversity and situated sociocultural theory, this article offers a case study of the mathematics engagement of Oscar, a fifth-grade student with autism, over the duration of 1 school year. Using field notes, videotapes of classroom interactions, student work, and teacher and student interviews, we examined the influence of the classroom activity system on this student’s participation in mathematical reasoning and discourse before and after a classroom intervention targeted to improve student engagement by making participation norms more explicit. Prior to the classroom intervention, Oscar did not participate verbally in small-group or whole-group mathematical discussion. After the classroom intervention, along with additional scaffolds such as increased peer accountability and collaborative strategy shares, Oscar increased his verbal and nonverbal participation in both small- and whole-group discussion. Through our year-long study, Oscar shifted from a student who did not speak in math class to one who explained his mathematical thinking in multiple contexts. We call for additional qualitative research in mathematics that seeks to understand the unique participation of students with autism, seeking understanding of how to better include these students in the Standards for Mathematical Practice. (PsycINFO Database Record (c) 2020 APA, all rights reserved)

Research Commentary: Unpacking the Links Between Equitable Teaching Practices and Standards for Mathematical Practice: Equity for Whom and Under What Conditions?

In their commentary, “Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice,” Bartell et al. (2017) provide a stepping-stone into the challenge of clarifying the interface between equity and standards setting in mathematics education by devising a framework that relates the Common Core State Standards for Mathematics to an explicit articulation of equitable teaching practices. In this commentary, we respond to this proposed framework and aim to clarify some key elements. Furthermore, we draw on our own positionings and scholarly interests to critique and bolster the framework by focusing on the tensions related to co-opting the Common Core for equity-oriented purposes, the framework's relationship to neoliberalism, and the role of racialized rhetoric and nondominant family and community knowledge.

Another encounter with the Alien Numbers problem

Students must actively engage in exploring math. That is why I am always looking for tasks that will allow my students to to explore problems using the Common Core's (CCSSI 2010) eight Standards for Mathematical Practice (SMP). These standards are vital for developing a deepening understanding of math. They allow students to cultivate skills and thought processes that aid in wiring their brains into being deep thinkers and problem solvers. These skills transcend the classroom and are needed to be successful in the world. I also want my students to revisit ideas that we have already touched on and continue to examine.

Questions to Elicit Students' Mathematical Ideas

Create opportunities for students to engage in the Standards for Mathematical Practice and support them in further explaining and justifying their ideas.

Transitioning from practicing teacher to teacher leader: a case study

ABSTRACTGiven US students’ lack of international competitiveness in mathematics and science, many states have adopted the Common Core State Standards for Mathematics (CCSSM). To help ensure that the Standards for Mathematical Practice within the CCSSM and effective teaching practices are implemented appropriately, many teachers are emerging as teacher leaders with the intent of supporting teachers with this implementation. Unfortunately, not all of these teachers are necessarily prepared in the field of teacher leadership. Recognizing the importance of having well-prepared teacher leaders, this article describes the case of Ms. Hodges, as she transitioned from mathematics teacher to teacher leader. Data revealed that several factors affected Ms. Hodges’ transition, some positively and others negatively. These results as well as implications for teacher leader development are provided.

Talking with Our Hands

In the elementary mathematics classroom, the pursuit of meaning may take many forms, including how we communicate with our physical movements. Often, mathematical communication is organized around verbalization. For example, teachers are often encouraged to facilitate productive mathematical discourse among students (CCSSI 2010; Stein et al. 2008). Similarly, the spoken words of the teacher carry great importance as she or he elects to revoice certain strategies as stated and perhaps verbally modify the language of others to enhance their clarity for the entire class. Such verbal interactions are, indeed, quite important regarding the construction of meaning; but we cannot neglect the nonverbal, physical manner in which we communicate with students. As we will see in subsequent examples, such nonverbal communication plays a role in students' construction of mathematical arguments and critiquing the reasoning of others—the third of the Common Core's (CCSSI 2010, pp. 6-7) Standards for Mathematical Practice (SMP 3)—as well as teachers' facilitation of meaningful mathematical discourse—the fourth of NCTM's Mathematics Teaching Practices (NCTM 2014, p. 10). To put it succinctly, it is well worth our while to consider how we, as a learning community, talk with our hands.

U.S. Middle School Mathematics Teachers’ Perceptions of the Standards for Mathematical Practice by Textbook Type

An important component of the Common Core State Standards for Mathematics (CCSSM), used by the majority of states in the U.S., are the eight standards for mathematical practice (SMPs). While surveys have investigated teachers’ perceptions of the CCSSM few have investigated middle school mathematics teachers’ (MSMTs’) (grades 6-8) perceptions of the SMPs. Similar to other countries, teachers in the United States frequently use mathematics textbooks. Two different types of textbooks have been in use in the United States, conventional and standards-based. The latter were designed on the basis of earlier standards documents including versions of the SMPs. As a result of these changes to the educational system in the U.S., we sought to characterize MSMTs’ perceptions of the SMPs and investigate if these perceptions differed by the type of textbook teachers used. We found that MSMTs struggled in naming the SMPs, misinterpreted the modeling SMP, and conflated components of reform-oriented instruction with the SMPs. MSMTs using a standards-based textbook were more likely to view their textbooks as aligned with the SMPs, and to view the SMPs as an instructional philosophy for the CCSSM, Fisher’s Exact Test = 3.881, p = .05. The implications of these results are discussed.

But What if the Goal is to Model with Mathematics?

odeling mathematics has a longstanding tradition in the mathematics classroom, as teachers often engage students in representing mathematical ideas. For example, students can be seen using base-ten blocks to model a number or drawing an array to represent a multiplication fact. Modeling a mathematical idea in this way, however, does not necessarily meet the expectations described in the fourth of the Common Core's Standards for Mathematical Practice (SMP 4): Model with mathematics, which states that students should “apply the mathematics they know to solve problems arising in everyday life, society, and the workplace” (CCSSI 2010, p. 7). Although the SMP provide a detailed description of modeling with mathematics, Bleiler-Baxter et al. (2017) found it useful to consider three decision-making processes embedded within the modeling process.

A validation process for observation protocols: Using the Revised SMPs Look-for Protocol as a lens on teachers’ promotion of the standards

ABSTRACTThe Standards for Mathematical Practice (SMPs) describe mathematical behaviors and habits that students should express during mathematics instruction. Thus teachers should promote them during classroom-based mathematics instruction. The purpose of this article is to discuss the validation process for an observation protocol called the Revised SMPs Look-for Protocol. An implication of this study is that users with a robust understanding of the SMPs may feel confident using the protocol as a validated and reliable tool in research and school-based settings. We discuss opportunities and challenges for mathematics teacher educators engaging in classroom observations, in light of this observation protocol.

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Its Impact on the Instructional Environment

This study examines Middle School Mathematics Teachers’ (MSMTs') (N = 1,241) perceptions of the Common Core State Standards for Mathematics (CCSSM) and its impact on the instructional environment. A total of eight factors appear in the data. These factors include professional support, teachers’ use of district‐adopted and non‐district‐adopted curricular resources, influence of CCSSM assessment and teacher evaluation on the instructional environment, influence of the CCSSM on classroom instruction, teachers’ planning practices, and perceived rigor of the CCSSM. The data suggest that teachers’ use of digital resources located online was disconnected from their district‐adopted resources suggesting a lack of curricular coherence. MSMTs note that the CCSSM had caused them to incorporate more reform‐oriented practices such as exploration and productive struggle into their daily instruction. MSMTs also perceive that the CCSSM includes new content that is more rigorous than previous state standards. Sampled MSMTs state that while state assessments will measure CCSSM content, they are less likely to include more complex problems or the standards for mathematical practice. Teachers are more likely to read teacher resources than student textbook activities online and to use digital resources for remediation instead of inquiry activities. Over one‐third of MSMTs wanted more CCSSM professional development.

Number Strings: Daily Computational Fluency

Second graders use this beneficial instructional routine alongside the Standards for Mathematical Practice.

Teaching Problem-Posing and Inquiry to Teachers Using a Non-Traditional Operation

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach pre-service and in-service teachers inquiry and problem-posing. We present a brief mathematical solution for the problem and we then discuss problem-posing activities and discussions of connections to the Standards of Mathematical Practice from the Common Core State Standards. We discuss several key aspects of the problem that make it well-suited for the purposes of teaching inquiry and problem-posing.

A Comparison of The Mathematical Processes Embedded in The Content Standards of Turkey and Singapore

This study compares Turkey's and Singapore's mathematics content standards in terms of the highligthed mathematical processes. A mathematical processes framework was employed to analyze the content standards drawing on the standards for mathematical practice defined by the Common Core State Standards for Mathematics. The standards for mathematical practice include make sense of problems and persevere in solving them, reason abstractly and quantitatively, construct viable arguments and critique the reasoning of others, model with mathematics, use appropriate tools strategically, attend to precision, look for and make use of structure, look for and express regularity in repeated reasoning. The data sources are 2013 mathematics curriculum standards of Turkey and 2013 mathematics syllabus of Singapore for grades 7 and 8. Data analysis revealed that the two countries reflected mathematical processes differently in their content standards. Some mathematical processes are not identified in Turkey's content standards while all mathematical processes are observed in Singapore's content standards. The distribution of the observed mathematical processes are also different in the two countries. Suggestions for future content standards revisions are shared in the paper.