K-12 Teaching and Learning From the UNC School of Education

Important Announcement about Online Courses and LEARN NC.

Important Message about LEARN NC

LEARN NC is evaluating its role in the current online education environment as it relates directly to the mission of UNC-Chapel Hill School of Education (UNC-CH SOE). We plan to look at our ability to facilitate the transmission of the best research coming out of UNC-CH SOE and other campus partners to support classroom teachers across North Carolina. We will begin by evaluating our existing faculty and student involvement with various NC public schools to determine what might be useful to share with you.

Don’t worry! The lesson plans, articles, and textbooks you use and love aren’t going away. They are simply being moved into the new LEARN NC Digital Archive. While we are moving away from a focus on publishing, we know it’s important that educators have access to these kinds of resources. These resources will be preserved on our website for the foreseeable future. That said, we’re directing our resources into our newest efforts, so we won’t be adding to the archive or updating its contents. This means that as the North Carolina Standard Course of Study changes in the future, we won’t be re-aligning resources. Our full-text and tag searches should make it possible for you to find exactly what you need, regardless of standards alignment.

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Related pages

  • The problem-centered classroom: A look inside an eighth-grade classroom in which students work in pairs to solve problems, then debate as a class which solution is correct or easiest. An explanation of the teaching method is provided along with video of students presenting their solutions to problems.
  • Science students get their hands dirty: Enter Carol Swink's classroom where students become scientists by conducting hands-on, inquiry-based investigations. By saving the textbook reading and lectures for last and doing experiments first, students master not only science content but math content too.
  • Student presentations in the problem-centered classroom : The video clip below shows students presenting their solutions to a math problem. The students worked...

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One of the goals of mathematics instruction is to prepare students to be problem solvers in a world where they will encounter complicated issues. The Common Core State Standards for Mathematics include problem-solving as the first of their Standards for Mathematical Practice. A problem-centered approach provides a vehicle to achieve the goals and objectives identified in the curriculum. Evidence from research and international studies suggests that our students are proficient in procedures but do not have the conceptual understanding to solve problems. The world they will live and work in will require them to gather, organize, and interpret data in the process of finding solutions to complex problems. It would seem only logical to provide a classroom setting where they will face similar issues. In the real world, the problems they face will not be ones for which they are selecting answers from a set of multiple choices.

The authentic type of problem is found primarily in enrichment programs or activities such as Science Olympiads and Odyssey of the Mind competitions. Typical problems in school mathematics tend to provide all the information needed and often anticipate that students will use a practiced procedure or formula to arrive at a single solution. The revisions of the End-of-Grade and End-of-Course tests in North Carolina have increased the level of cognitive demand by including more items that require a variety of problem-solving strategies. Teachers who have reviewed these instruments have commented on the need to provide more problem-centered instruction.

The role of a classroom teacher is that of an active problem solver making instructional decisions with a constant influx of data from a variety of sources. An effective classroom teacher must design experiences that enable students to achieve designated objectives and must orchestrate students’ work as they progress through those experiences. These experiences must be founded on the ways in which students develop mathematical understanding. Students build mathematical understanding when they are required to build new knowledge by pondering, creating, and critiquing arguments about mathematics.

Students must experience problems where flexible use of knowledge is required. No mathematical thinking is required for tasks in which a routine is used to provide a solution that is known in advance. Directed and focused questions must challenge students to select from a variety of strategies. Students need to analyze problems, determine what information is needed to solve them, and design solutions. Appropriate tasks should engage all students and provide opportunities for extensions that encourage students to go beyond minimum expectations. The teacher becomes a tutor or coach who facilitates the students’ investigations.

Problem solving must be more than routine exercises. It cannot be viewed as an "add on" to classroom instruction but rather an important goal. Problem solving should be viewed as a means to mathematical understanding as well as a set of procedures. Engaging students in problem-centered learning will allow students to see connections within and between content areas. Students will develop the ability to employ and select appropriateness of a variety of strategies for designing solutions. Problem-centered learning creates a model where the student becomes the thinker and is engaged in a self-directed search for solutions.