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Technology will not inherently make students in any classroom more mathematically inquisitive, however, the use of technology can foster student-centered inquiry. This article explores the impact technology has on mathematics learning when it emphasizes the ways it supports student-centered pedagogies. Through this lens, the authors focus on implementing tasks that promote reasoning and problem solving (National Council of Teachers of Mathematics [NCTM], 2000, 2014) through the mathematical action technology of GeoGebra and its opportunity for dynamic manipulation of shapes to support the lesson's goals, including mathematical reasoning and conversations, as students explore the Pythagorean theorem. Because the technology alleviates area calculations, the tasks promote equal opportunity by leveling the field for students to access the standard. Embedded into the task's design, GeoGebra supports promoting cycles of proof: creating, testing, revising, and proving mathematical conjectures (Cullen et al., 2020) because students use the technology to test and revise their initial conjectures on the validity of a Pythagorean theorem extension for similar figures.

How can a cognitively demanding real-world task such as the Seven Billion People problem promote productive struggle "and" help shape students' mathematical dispositions? Driving home from school one evening, Jaclyn Murawska heard a commentator on the radio announce three statements: (1) experts had determined that the world population had reached 7 billion people; (2) if you laid out all the people on earth end to end, they would circle the earth 266 times; and (3) if all 7 billion people stood shoulder to shoulder, they would all fit into Los Angeles. Skeptical of the veracity of the latter two claims, Murawska went to work verifying them, which required making assumptions, performing some estimation, converting units within a measurement system, and doing calculations with circumference and area (i.e., using the Common Core's standards 4.MD.1, 5.MD.1, and 7.G.B.4; CCSSI 2010). Surprisingly she found that both the last two statements were reasonable. In this article, she explores to what extent this task would elicit productive struggle in her preservice elementary- and middle-level teachers.

In this commentary, we offer a set of visual tools that can assist education researchers, especially those in the field of mathematics, in developing cohesiveness from a mixed methods perspective, commencing at a study's research questions and literature review, through its data collection and analysis, and finally to its results. This expounds upon the ideas and methodological insights relating to research connections and structure presented by other scholars (e.g., Creswell, 2009; Heid & Blume, 2011; Mertens, 2010; Thanheiser, Ellis, & Herbel-Eisenmann, 2012). As faculty who work with graduate students in education, we have found that these visual tools help students elicit and maintain salient connections throughout the research process.

Sometimes the best mathematics problems come from the most unexpected situations. Last summer, a Corvette raced down a local quarter-mile drag strip. The driver, a family member, provided the spectators with time and distance-traveled data from his time slip and asked "Can you calculate how many seconds it took me to go from 0 to 60 mph?" Although initially this question seemed like a straightforward one, it was soon clear that depending on the solution strategy and assumptions, different answers were possible. Thus began the ongoing discussions with colleagues--and with high school mathematics teacher friends over pizza and with mechanical engineer family members at holiday dinners--to collectively decide on the "best" method. The mathematical discussions that arose on how to best solve the problem prompted two questions: (1) What makes this problem so intriguing? and (2) What would students do? Any interesting mathematical task will likely encourage teachers to wonder what aspects of the task make it special. The authors of this article wanted to know why this problem generated these mathematical conversations and how they could incorporate it into a calculus class. Insights from colleagues and students revealed several qualities of the problem that they believe contribute to its intrigue and worth. What they found illustrates what they consider to be three hallmarks of a good problem: (1) The problem solver must decide what mathematics to introduce; (2) The task users real-life data; and (3) The task requires mathematical modeling. A nonroutine task with three hallmarks of a good problem offers the flexibility to model real-life, messy data.

Although discussions about inductive reasoning can be traced back thousands of years (Fitelson 2011), the implementation of the Standards for Mathematical Practice (SMP) within the Common Core State Standards (CCSSI 2010) is generating renewed attention to how students learn mathematics. The third SMP, "Construct viable arguments and critique the reasoning of others" (CCSSI 2010, p. 6), explicitly calls for mathematically proficient students to be able to reason inductively and be able to judge the validity of their conclusions. NCTM (2000, p. 16) also emphasizes that middle school students should be "proficient in using inductive and deductive reasoning appropriately." The development of these reasoning skills can help promote students' conceptual understanding, linking conceptual knowledge and procedural knowledge (Hiebert and Lefevre 1996; NCTM 2000). Hence, to align with national standards and promote conceptual understanding, middle school mathematics educators should provide ample opportunities for students to engage in inductive reasoning activities that can build to deductive reasoning. The series of tasks proposed in this article encourages students to reason inductively and uses problem solving with multiple representations, supported by current mathematics education standards (CCSSI 2010; NCTM 2000). Because the tasks are undergirded by science education inquiry, these tasks support recent STEM literacy initiatives, as well (Zollman 2012).

In this commentary, we offer a set of visual tools that can assist education researchers, especially those in the field of mathematics, in developing cohesiveness from a mixed methods perspective, commencing at a study's research questions and literature review, through its data collection and analysis, and finally to its results. This expounds upon the ideas and methodological insights relating to research connections and structure presented by other scholars (e.g., Creswell, 2009; Heid & Blume, 2011; Mertens, 2010; Thanheiser, Ellis, & Herbel-Eisenmann, 2012). As faculty who work with graduate students in education, we have found that these visual tools help students elicit and maintain salient connections throughout the research process. [ABSTRACT FROM AUTHOR]

The article presents the author's views about the influence of the Common Core State Standards (CCSS) on K-12 and college mathematics education in the U.S. Topics include the origin of CCSS, the effectiveness of the Standards for Mathematical Practice (SMP) under the CCSS for Mathematics and the lessons that can be learned by college mathematics instructors from the CCSS.