This program uses standards provided by the National Council of Teachers of Mathematics (NCTM).
Graduates earning a master’s degree in mathematics instructional leadership from Hood College:
- Effective teachers of secondary mathematics demonstrate and apply knowledge of major mathematics concepts, algorithms, procedures, connections, and applications within and among mathematical content domains through:
Effective teachers of secondary mathematics solve problems, represent mathematical ideas, reason, prove, use mathematical models, attend to precision, identify elements of structure, generalize, engage in mathematical communication and make connections as essential mathematical practices. They understand that these practices intersect with mathematical content and that understanding relies on the ability to demonstrate these practices within and among mathematical domains and in their teaching through:
- Demonstrating and applying knowledge of major mathematics concepts, algorithms, procedures, applications in varied contexts, and connections within and among mathematical domains (Number, Algebra, Geometry, Trigonometry, Statistics, Probability, Calculus and Discrete Mathematics) as outlined in the NCTM CAEP Mathematics Content for Secondary.
Effective teachers of secondary mathematics apply knowledge of curriculum standards for mathematics and their relationship to student learning within and across mathematical domains. They incorporate research-based mathematical experiences and include multiple instructional strategies and mathematics-specific technological tools in their teaching to develop all students’ mathematical understanding and proficiency. They provide students with opportunities to do mathematics – talking about it and connecting it to both theoretical and real-world contexts. They plan, select, implement, interpret and use formative and summative assessments for monitoring student learning, measuring student mathematical understanding, and informing practice through:
- Using problem solving to develop conceptual understanding, make sense of a wide variety of problems and persevere in solving them, apply and adapt a variety of strategies in solving problems confronted within the field of mathematics and other contexts and formulate and test conjectures in order to frame generalizations;
- Reasoning abstractly, reflectively and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others; represent and model generalizations using mathematics; recognize structure and express regularity in patterns of mathematical reasoning; use multiple representations to model and describe mathematics; and utilize appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others;
- Formulating, representing, analyzing and interpreting mathematical models derived from real-world contexts or mathematical problems;
- Organizing mathematical thinking and use the language of mathematics to express ideas precisely, both orally and in writing to multiple audiences;
- Demonstrating the interconnectedness of mathematical ideas and how they build on one another and recognize and apply mathematical connections among mathematical ideas and across various content areas and real-world contexts; and
- Modeling how the development of mathematical understanding within and among mathematical domains intersects with the mathematical practices of problem solving, reasoning, communicating, connecting and representing.
Plan, select, implement, interpret and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students through:
- Applying knowledge of curriculum standards for secondary mathematics and their relationship to student learning within and across mathematical domains;
- Analyzing and considering research in planning for and leading students in rich mathematical learning experiences;
- Planning lessons and units that incorporate a variety of strategies, differentiated instruction for diverse populations and mathematics-specific and instructional technologies in building all students’ conceptual understanding and procedural proficiency;
- Providing students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life and the workplace; and
- Implementing techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions and employing a range of questioning strategies.
Effective teachers of secondary mathematics exhibit knowledge of adolescent learning, development and behavior. They use this knowledge to plan and create sequential learning opportunities grounded in mathematics education research where students are actively engaged in the mathematics they are learning and building from prior knowledge and skills. They demonstrate a positive disposition toward mathematical practices and learning, include culturally relevant perspectives in teaching and demonstrate equitable and ethical treatment of and high expectations for all students. They use instructional tools such as manipulatives, digital tools and virtual resources to enhance learning while recognizing the possible limitations of such tools through:
- Monitoring students’ progress, making instructional decisions and measuring students’ mathematical understanding and ability using formative and summative assessments.
Effective teachers of secondary mathematics provide evidence demonstrating that as a result of their instruction, secondary students’ conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and application of major mathematics concepts in varied contexts have increased. These teachers support the continual development of a productive disposition toward mathematics. They show that new student mathematical knowledge has been created as a consequence of their ability to engage students in mathematical experiences that are developmentally appropriate, require active engagement and include mathematics-specific technology in building new knowledge through:
- Exhibiting knowledge of adolescent learning, development and behavior and demonstrate a positive disposition toward mathematical processes and learning;
- Planning and creating developmentally appropriate, sequential and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences;
- Incorporating knowledge of individual differences and the cultural and language diversity that exists within classrooms and include culturally relevant perspectives as a means to motivate and engage students;
- Demonstrating equitable and ethical treatment of and high expectations for all students; and
- Applying mathematical content and pedagogical knowledge to select and use instructional tools such as manipulatives and physical models, drawings, virtual environments, spreadsheets, presentation tools and mathematics-specific technologies (e.g., graphing tools, interactive geometry software, computer algebra systems and statistical packages); and make sound decisions about when such tools enhance teaching and learning, recognizing both the insights to be gained and possible limitations of such tools.
Effective teachers of secondary mathematics are lifelong learners and recognize that learning is often collaborative. They participate in professional development experiences specific to mathematics and mathematics education, draw upon mathematics education research to inform practice, continuously reflect on their practice and utilize resources from professional mathematics organizations through:
- Verifying that secondary students demonstrate conceptual understanding; procedural fluency; the ability to formulate, represent and solve problems; logical reasoning and continuous reflection on that reasoning; productive disposition toward mathematics; and the application of mathematics in a variety of contexts within major mathematical domains;
- Engaging students in developmentally appropriate mathematical activities and investigations that require active engagement and include mathematics-specific technology in building new knowledge; and
- Collecting, organizing, analyzing and reflecting on diagnostic, formative and summative assessment evidence and determine the extent to which students’ mathematical proficiencies have increased as a result of their instruction.
Effective teachers of secondary mathematics engage in a planned sequence of field experiences and clinical practice under the supervision of experienced and highly qualified mathematics teachers. They develop a broad experiential base of knowledge, skills, effective approaches to mathematics teaching and learning and professional behaviors across both middle and high school settings that involve a diverse range and varied groupings of students. Candidates experience a full-time student teaching/internship in secondary mathematics directed by university or college faculty with secondary mathematics teaching experience or equivalent knowledge base through:
- Taking an active role in their professional growth by participating in professional development experiences that directly relate to the learning and teaching of mathematics;
- Engaging in continuous and collaborative learning that draws upon research in mathematics education to inform practice; enhance learning opportunities for all students’ mathematical knowledge development; involve colleagues, other school professionals, families, and various stakeholders; and advance their development as a reflective practitioner; and
- Utilizing resources from professional mathematics education organizations such as print, digital and virtual resources/collections.
- Engaging in a sequence of planned field experiences and clinical practice prior to a full-time student teaching/internship experience that include observing and participating in both middle and high school mathematics classrooms and working with a diverse range of students individually, in small groups, and in large class settings under the supervision of experienced and highly qualified mathematics teachers in varied settings that reflect cultural, ethnic, linguistic, gender and learning differences;
- Experiencing full-time student teaching/internship in secondary mathematics that is supervised by a highly qualified mathematics teacher and a university or college supervisor with secondary mathematics teaching experience or equivalent knowledge base; and
- Developing knowledge, skills, and professional behaviors across both middle and high school settings; examine the nature of mathematics, how mathematics should be taught and how students learn mathematics; and observe and analyze a range of approaches to mathematics teaching and learning, focusing on tasks, discourse, environment and assessment.