Mathematics

Why study mathematics?

Mathematics provides people a unique, yet universal way of understanding, interpreting and communicating about the world and our experiences in it.

Today, we rely on mathematics in ways that were unfathomable just a few decades ago. From innovations in communications and medicine to understanding our environment, and to managing everyday life experiences, mathematics touches our lives in so many ways, seen and unseen.

For our children to be able to take advantage of opportunities and overcome challenges in our fast-changing world, it is critical that we engage students in meaningful learning opportunities integrated with science and technology that help students to see mathematics as a powerful, useful, sense-making tool. Through the study of mathematics, we help students:

  • cultivate their talents, their character, and their aspirations
  • use math to solve problems, make sense of the world, make informed decisions in their lives and be critical consumers of information
  • develop their voice as learners and community members
  • appreciate both the utility and the beauty of mathematics

Core principles of mathematics

The grades K-12 progression of mathematics learning expectations in the Hawaiʻi Core Standards is designed so that every student in the State of Hawaiʻi can achieve mathematical competence through a curriculum that emphasizes literacy, sense-making, problem-solving, communication, the strategic use of technology and the application of mathematics in real- world contexts and to other disciplines.

To ensure that students from all racial, ethnic, linguistic, gender, and socioeconomic groups meet the Hawaii Core Standards, schools must establish a culture of access and equity.

  • Math teachers work collaboratively with special education and English language teachers, and colleagues across disciplines to build effective teaching practices that close the achievement gap (NCTM, 2018).
  • Students routinely have opportunities to experience high-quality differentiated instruction and learn rigorous mathematics content in a safe learning environment that promotes creativity, collaboration, and a growth mindset (Emersonkress, 2015).
  • Teachers regularly monitor student progress and make strategic real-time adjustments to support and optimize student learning.

The Hawaiʻi Core Standards for mathematics has two equally important sets of expectations: the Standards for Mathematical Practice and the content standards.

Standards for mathematical practice

  • describe the various types of expertise and habits of mind that students should develop as they engage with mathematics. They describe what we want to see STUDENTS doing as they engage with mathematics. “Encouraging these practices in students of all ages should be as much a goal of the mathematics curriculum as the learning of specific content” (Common Core State Standards Initiative, 2010).
  • should inform teachers’ decision-making when planning learning opportunities for students and when creating class norms and structures that promote a culture for learning in the mathematics classroom. Formative feedback will be constructive to promote student growth regarding the Practices; however, a summative grade should not be given regarding the Practices.

Content standards

The design principles for the content standards (often referred to as “the three shifts”) are focus, coherence, and rigor (Achievethecore.org).

  1. Focus: Each grade level has “critical areas of focus” that inform teachers of the high-priority learning targets for that grade level. Teachers should FOCUS on the high-priority learning targets for their grade, devoting more learning time to address the depth of these standards.
  2. Coherence: The Common Core standards are a progression across grade levels. Concepts and skills scaffold from one grade to the next. Instruction should intentionally relate new concepts to students’ prior skills and knowledge (across grade levels). Additionally, within a grade level, teachers should intentionally make connections between related concepts (e.g., multiplication and area in grade 3, or statistics and functions in grades 8 and 9).
  3. Rigor: The balance between conceptual understanding, fluency with skills and procedures, and application. The 8 Standards for Mathematical Practice are critical to ensuring that RIGOR is in the mathematics classroom.

The National Council of Teachers of Mathematics asserts the following eight teaching practices that research indicates need to be consistent components of the teaching and learning opportunities that are designed to engage students with mathematics (NCTM, 2014):

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

Where is Mathematics headed?

Mathematics classrooms should be caring environments where active engagement, inquiry, a culture that promotes discourse and sense-making, a culture that promotes a habit of self-reflection and learning from one’s mistakes is pervasive.

Promoting a well-rounded education for all students compels the Department to promote opportunities for teachers to gain the knowledge and experiences that will equip them to incorporate teaching and learning experiences that meaningfully connect various disciplines and provide opportunities to incorporate students’ voice and choice.

As a result, there is growing focus and need on project-based learning and STEM. The importance of developing and using models to solve problems, constructing viable arguments based on evidence, and critiquing the reasoning of others, as described in the Mathematical Practices, cuts across many disciplines. This is a common thread through STEM education.

As mathematics is integrated, it is important to keep in mind that we must maintain the integrity of the standards so that students develop a full understanding of concepts and are equipped to pursue post-secondary STEM majors and careers.

Ensuring the mathematics is on grade-level, addressed conceptually, and has a coherent mathematical progression allows students to learn mathematics not only for the workplace and for the scientific and technical communities, but also empowers ALL students in their personal lives, whether or not they choose to continue in a STEM-related field. (Larson, 2017)

The field of ethnomathematics is an example of a unique opportunity to support teachers to integrate STEM perspectives and culturally-responsive pedagogy into their curricula. Over the past several years, the University of Hawaiʻi’s Ethnomathematics Institute has provided teachers with opportunities to be purposeful in helping students to develop the skills, behaviors, and dispositions that are representative of the unique characteristics of the culture of Hawaiʻi, which is the vision of HIDOE’s Nā Hopena Aʻo (HĀ) framework. Utilizing the resources, lessons, and perspectives promoted by the Ethnomathematics Institute has the potential to empower teachers and support their efforts to improve students’ academic achievement while inspiring their students and developing their character and social-emotional well-being in ways that genuinely represent the core values and beliefs of the Department.

Mathematics resources

References
Catalyzing change in high school mathematics: Initiating critical conversations. (2018). Reston, VA: The National Council of Teachers of Mathematics.
Emersonkress, N. (2015, March 05). 8 Characteristics of an Equitable Mathematics Classroom. Retrieved from https://mathisforeveryone.wordpress.com/2015/03/05/8-characteristics-of-an-equitable-mathematics-classroom/
Larson, M. (2017, May 17). Math Education Is STEM Education! Retrieved from https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Matt-Larson/Math-Education-Is-STEM-Education!/
Principles to actions: Ensuring mathematical success for all. (2014). Reston, VA: NCTM, National Council of Teachers of Mathematics.