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Mathematics Curriculum

A joint position of the Hoosier Association of Mathematics Teacher Educators (HAMTE) and the Indiana Council of Teachers of Mathematics (ICTM)

HAMTE/ICTM Position

According to the National Council of Teachers of Mathematics (NCTM, 2014), “An excellent mathematics program includes a curriculum that develops important mathematics along coherent learning progressions and develops connections among areas of mathematical study and between mathematics and the real world” (p. 70). We believe that all Indiana students should have equitable access to excellent mathematics programs in their schools.

It is important to distinguish between standards and curriculum. Standards are statements of what students are expected to achieve at grade band levels. A curriculum is a program used to help students meet the expectations set forth by the standards, including recommended instructional materials, activities, tasks, lessons, units, and assessments (NCTM, 2014).

Obstacles

We support the goal of excellent mathematics curricula for all Indiana schools, but we recognize potential obstacles that currently pose a threat to the realization of that goal.

Standards. The Indiana Academic Standards for Mathematics, approved in April 2014, state what students should know and be able to do in the areas of K-8 Mathematics; Algebra I, II, and Geometry; and higher-level high school mathematics. It is expected that teachers will use these standards to guide their curricula. Each standards document includes mathematics process standards that span grades K-12 and mathematics content standards that are grade-level- or course-specific. The mathematics content standards were developed with some attention to research-based learning progressions that describe what is known about how students’ mathematical knowledge, skills, and understanding develop over time. However, because these developmental progressions are not evident in the standards’ format, the standards are often treated as checklists of topics. When regarded in this light, mathematics content only becomes a set of isolated skills, often without a mathematical or real-world context (NCTM, 2014).

Curriculum materials. In Indiana, the adoption of curricular materials is guided by a public law (PL 73-2011) that gives local school districts freedom to set their own criteria for textbook (or alternative materials) adoption. Some schools have chosen to adopt print or digital textbooks and others have chosen to use their textbook funds to purchase tablets or computers, leaving teachers to develop their own instructional materials, scope and sequence. Textbooks provide support for teachers through a carefully designed scope and sequence of topics and relative instructional resources. They provide support for students though their definitions, diagrams, examples, problem sets, and consistent use of content specific language and symbols. However, mathematics textbooks vary greatly in the treatment of critical aspects of curriculum. Some textbooks are designed to focus on big mathematical ideas, to develop those ideas through

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learning progressions, to emphasize connections among topics, and to engage students in mathematical processes related to real world applications; other textbooks are less effectively designed (NCTM, 2014). In schools that have moved away from the use of textbooks, teachers are relegated to design their own curriculum by time consuming searches for external resources and learning materials, development of activities and lessons, and design of assessments that are relative to their instruction. With so much responsibility for orchestrating a learning environment and constructive experiences, it remains uncertain how adequate these learning experiences are designed to support optimal learning for students.

Overcoming the Obstacles

Overcoming these obstacles requires careful attention to curriculum design and implementation.

Curriculum design. The design of a curriculum implies more than a collection of activities. It requires a coherent sequencing of core mathematical ideas that are well articulated within and across grades and courses. Curriculum design must take into consideration the amount of new content to be introduced in each grade or course so that sufficient time is available to develop concepts and procedures through the following Mathematics Teaching Practices (NCTM, 2014):

Establish mathematics goals to focus learning; Implement tasks that promote reasoning and problem solving; Use and connect mathematical representations; Facilitate meaningful mathematical discourse; Pose purposeful questions; Build procedural fluency from conceptual understanding; Support productive struggle in learning mathematics; and Elicit and use evidence of student thinking.

Curriculum implementation. Teachers who are well prepared in their knowledge of mathematics content and the development of students’ mathematical thinking are equipped to implement an effective mathematics curriculum, one that engages students in mathematics processes and helps them connect concepts and procedures to strengthen their understanding (NCTM, 2014). Instructional materials and tasks implemented by teachers have a significant influence on what mathematics students learn and how they learn it (Stein, Remillard, & Smith, 2007). Continual high-quality professional development for teachers is essential to maximize the effectiveness of curriculum materials, since even the best textbooks and resources can be misinterpreted or misused (NCTM, 2014).

Recommendations

To assure that all Indiana students have access to excellent and equitable mathematics learning opportunities in their schools, we recommend the following actions be taken by key stakeholders involved in mathematics programs in Indiana schools:

1. State leaders create documents to guide teachers in research-based learning progressions.

2. District leaders ensure that the mathematics curriculum reflects the importance of

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mathematical processes; supports and promotes conceptual understanding; and provides procedural fluency while applying real-world problems.

3. Principles, coaches, specialists, and other school leaders ensure that the process of selecting curriculum materials is collaborative and includes careful examination of the extent to which the materials not only align with the standards but also develop topics coherently within and across grade bands, promote the mathematical processes, and support effective instruction as characterized by the Mathematics Teaching Practices.

4. Teachers evaluate curricular materials and resources, including textbooks, collections of activities, and software, to determine the extent to which these materials align with the standards, ensure coherent development of topics within and across grade bands, promote the mathematical practices, and support effective instruction that implements the Mathematics Teaching Practices.

5. Teachers sequence tasks and activities with long-term goals in mind; when conducting lesson and unit planning, focus on connections among key mathematical ideas that are situated in real-world and mathematical contexts.

References

National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: NCTM.

Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-369). Charlotte, N.C.: Information Age; Reston, Va.: National Council of Teachers of Mathematics.