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Mathematics (STEM) careers rely on mathematics. The future demands of the STEM careers are in creasing, and salary growth in the STEM careers has increased. Mathematics is a part of various as pects of life both seen and unseen. Students need to be able to interpret, identify, evaluate, and critique the mathematics to make wise decisions in their personal lives. All students need to experience the beauty of mathematics and develop an understand ing of the importance that it has played in history and society (NCTM, 2018). One of the suggestions from “ Catalyzing Change ” was to discontinue the practice of tracking teachers and students into “ dead - end ” course pathways (NCTM, 2018). According to Boaler ’ s article on “ Changing Students ’ Lives through the De Tracking of Urban Mathematics Classrooms ”, tracking students places students in different course pathways which provides some students with ac cess to mathematics instructions to prepare them for postsecondary education while others will not be prepared. Tracking students reinforces that some students can do math and others cannot (Boaler, 2011). In Principles to Action (NCTM, 2014), “ An excellent mathematics program requires that all students have access to a high - quality mathematics curriculum, effective teaching and learning, high expectation and support, and resources needed to maximize their learning potential (p. 59)” (NCTM, 2018, p. 15). Equitable instructions consist of classroom instruc tions that are consistent with research and “ equitable teaching practices ” in which “ students develop a positive mathematical identi ties ” (NCTM, 2018, p. 25). The authors provided the “ Bike and Truck Task ” as an example of imple menting equitable instructions through developing students ’ mathematical identities that impact their environment. The example illustrated how Ms. Shackelford engaged her students in their reasoning and making sense of others ’ reasoning. She created a safe environment for all students to participate in Implementing Equitable Instruction Creating Equitable Structures

the class discussion. The norms and practices al lowed her students to be doers of mathematics (NCTM, 2018). In the Principles to Action (2014), the National Council of Teachers of Mathematics (NCTM) articulated the eight effective mathemat ics teaching practices as a “ framework for making connections between these high leverage teaching practices and the development of identity, agency, and competence ” (NCTM, 2018, p. 29). Improve ments in teaching practices needs to consider math ematical identities of students as “ knowers and do ers of mathematics ” (NCTM, 2018). Based on re search, “ equitable mathematics teaching practices are inclusive when they acknowledge that students bring knowledge and resources from their commu nities and make community - based knowledge and resources an integral part of mathematics teach ing ” (NCTM, 2018, p. 36). The importance of collaborating to support effec tive mathematics teaching practices is critical. Building teachers capacity by “ a key aspect of the ‘ Professional Principle ’ is recognizing that their own learning is never finished and that they must build a culture of professional collaboration that is driven by a sense of interdependence and collective responsibility ” (Berry and Berry, 2017) (NCTM, 2018, p. 35). Time and professional isolation hin der professional collaboration within high schools (Berry and Berry, 2017). When teachers do not col laborate, the “ professional isolation leads to incon sistencies in teaching practices, creating inequities in student learning ” (Feiman - Nemser, 2012) (NCTM, 2018, p. 35). The “ Essential Concepts ” that all students should learn include the following key content domains: number, algebra and functions, statistics and proba bility, and geometry and measurement (NCTM, 2018). The “ Essential Concepts ” should not be considered as a list of topics to be covered but as the key concepts within each content domain that have enduring value for students; mathematical un derstanding and their continued study of mathemat ics. The authors provide examples within context of essential concepts in number, algebra and func- “ Essential Concepts ”

Virginia Mathematics Teacher vol. 47, no. 1

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