A **three-part lesson** is an inquiry-based learning method used to teach mathematics in K–12 schools.

- Components
- Getting started phase (10 to 15 minutes)
- Work phase (30 to 40 minutes)
- Consolidation and practice phase (10 to 15 minutes)
- Effectiveness
- See also
- References

The three-part lesson has been attributed to John A. Van de Walle, a mathematician at Virginia Commonwealth University.^{ [1] }^{ [2] }

The purpose is to cognitively prepare students for the math lesson by having them think about a procedure, strategy or concept used in a prior lesson. Teachers determine what specific previous learning they wish students to recall, based on outcomes desired for that particular lesson.^{ [3] } The role of the teacher is to "get students mentally prepared to work on the problem".^{ [1] }

Marian Small, a proponent of a constructivist approach to mathematical instruction, provides an example of an inquiry-based question from which a three-part lesson could be created: "one bus has 47 students in it; another has 38. How many students are on both buses?"^{ [4] }

Students engage in solving math problems individually, in pairs, or in small groups, and "record the mathematical thinking they used to develop solutions". Students then plan the strategies, methods, and concrete materials they will use to solve the problem. The teacher will circulate and make observations about the ways students are interacting, and will note the mathematical language they are using as well as the mathematical models they are employing to solve the problem. If a student is having difficulty, "the teacher might pose questions to provoke further thinking or have other students explain their plan for solving the problem".^{ [3] } Teachers are advised to be active listeners in this phase, and to take notes. This is also a phase in which teachers can assess students.^{ [1] }

In this final phase, the teacher oversees the sharing of solutions by students, and may employ other teaching techniques such as "math congress", "gallery walk", or "bansho". If new methods and strategies were discovered by students during the work phase, the teacher will post these on the class's "strategy wall", or use them to develop an "anchor chart".^{ [3] } Teachers are not to evaluate students in this phase, but should be actively listening "to both good and not so good ideas".^{ [1] }

Advocates of the three-part lesson state that students develop "independence and confidence by choosing the methods, strategies and concrete materials they will use, as well as ways to record their solutions". They claim students learn to discern similarities and differences in the mathematics, and also that "through such rich mathematics classroom discourse, students develop and consolidate their understanding of the learning goal of the lesson in terms of making connections to prior knowledge and experiences and making generalizations".^{ [3] } Advocates also claim "students are more enthusiastic about the subject" when inquiry-based math instruction is used.^{ [5] }

Opponents of inquiry-based methods such as the three-part lesson state that students are not learning the basics such as multiplication tables. In Ontario, Canada, where the Ministry of Education has promoted the three-part lesson, the curriculum was changed in the late 1990s in favour of "problem solving based on open-ended investigations rather than memorization". In that province, test scores in grades three and grade six math declined between 2009 and 2013, and "some contend that the math curriculum rather than teacher education is to blame for the lower scores because it places more emphasis on real-world concepts and applications than on rote learning".^{ [5] }

A **teaching method** comprises the principles and methods used by teachers to enable student learning. These strategies are determined partly on subject matter to be taught and partly by the nature of the learner. For a particular teaching method to be appropriate and efficient it has to be in relation with the characteristic of the learner and the type of learning it is supposed to bring about. Suggestions are there to design and selection of teaching methods must take into account not only the nature of the subject matter but also how students learn. In today's school the trend is that it encourages much creativity. It is a known fact that human advancement comes through reasoning. This reasoning and original thought enhances creativity.

In contemporary education, **mathematics education** is the practice of teaching and learning mathematics, along with the associated scholarly research.

**Problem-based learning** (**PBL**) is a student-centered pedagogy in which students learn about a subject through the experience of solving an open-ended problem found in trigger material. The PBL process does not focus on problem solving with a defined solution, but it allows for the development of other desirable skills and attributes. This includes knowledge acquisition, enhanced group collaboration and communication.

**Constructivism** is a theory in education that recognizes learners *construct* new understandings and knowledge, integrating with what they already know. This includes knowledge gained prior to entering school. It is associated with various philosophical positions, particularly in epistemology as well as ontology, politics, and ethics. The origin of the theory is also linked to Jean Piaget's theory of cognitive development.

* Principles and Standards for School Mathematics* (

Founded in 1920, The **National Council of Teachers of Mathematics** (**NCTM**) is the world's largest mathematics education organization.

**Project-based learning** (**PBL**) is a student-centered pedagogy that involves a dynamic classroom approach in which it is believed that students acquire a deeper knowledge through active exploration of real-world challenges and problems. Students learn about a subject by working for an extended period of time to investigate and respond to a complex question, challenge, or problem. It is a style of active learning and inquiry-based learning. PBL contrasts with paper-based, rote memorization, or teacher-led instruction that presents established facts or portrays a smooth path to knowledge by instead posing questions, problems or scenarios.

**Saxon math**, developed by John Saxon (1923–1996), is a teaching method for incremental learning of mathematics created in the 1980s. It involves teaching a new mathematical concept every day and constantly reviewing old concepts. Early editions were deprecated for providing very few opportunities to practice the new material before plunging into a review of all previous material. Newer editions typically split the day's work evenly between practicing the new material and reviewing old material. It uses a steady review of all previous material, with a focus on students who struggle with retaining the math they previously learned. However, it has sometimes been criticized for its heavy emphasis on rote rather than conceptual learning.

**Discovery learning** is a technique of inquiry-based learning and is considered a constructivist based approach to education. It is also referred to as problem-based learning, experiential learning and 21st century learning. It is supported by the work of learning theorists and psychologists Jean Piaget, Jerome Bruner, and Seymour Papert.

**Formative assessment**, **formative evaluation**, **formative feedback**, or **assessment for learning**, including *diagnostic testing*, is a range of formal and informal assessment procedures conducted by teachers during the learning process in order to modify teaching and learning activities to improve student attainment. The goal of a formative assessment is to *monitor student learning* to provide ongoing feedback that can help students identify their strengths and weaknesses and target areas that need work. It also helps faculty recognize where students are struggling and address problems immediately. It typically involves qualitative feedback for both student and teacher that focuses on the details of content and performance. It is commonly contrasted with summative assessment, which seeks to monitor educational outcomes, often for purposes of external accountability.

**Core-Plus Mathematics** is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled *Contemporary Mathematics in Context: A Unified Approach*, was completed in 1995. The third edition, entitled *Core-Plus Mathematics: Contemporary Mathematics in Context*, was published by McGraw-Hill Education in 2015.

**Math wars** is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the *Curriculum and Evaluation Standards for School Mathematics* by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.

**Mathematical anxiety**, also known as **math phobia**, is anxiety about one's ability to do mathematics.

**Singapore math** is a teaching method based on the national mathematics curriculum used for Singaporean schools. The term was coined in the United States to describe an approach originally developed in Singapore to teach students to learn and master fewer mathematical concepts at greater detail as well as having them learn these concepts using a three-step learning process: concrete, pictorial, and abstract. In the concrete step, students engage in hands-on learning experiences using physical objects which can be everyday items such as paper clips, toy blocks or math manipulates such as counting bears, link cubes and fraction discs. This is followed by drawing pictorial representations of mathematical concepts. Students then solve mathematical problems in an abstract way by using numbers and symbols.

**Connected Mathematics** is a comprehensive mathematics program intended for U.S. students in grades 6-8. The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum developers, mathematicians, and mathematics education researchers.

**Reform mathematics** is an approach to mathematics education, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics (NCTM). The NCTM document, Curriculum and Evaluation Standards for School Mathematics, attempted to set forth a vision for K-12 mathematics education in the United States and Canada. Their recommendations were adopted by many education agencies, from local to federal levels through the 1990s. In 2000, NCTM revised its standards with the publication of Principles and Standards for School Mathematics (PSSM). Like the first publication, these updated standards have continued to serve as the basis for many states' mathematics standards, and for many federally funded textbook projects. The first standards gave a strong call for a de-emphasis on manual arithmetic in favor of students' discovering their own knowledge and conceptual thinking. The PSSM has taken a more balanced view, but still emphasizes conceptual thinking and problem solving.

**Inquiry-based learning** is a form of active learning that starts by posing questions, problems or scenarios. It contrasts with traditional education, which generally relies on the teacher presenting facts and their own knowledge about the subject. Inquiry-based learning is often assisted by a facilitator rather than a lecturer. Inquirers will identify and research issues and questions to develop knowledge or solutions. Inquiry-based learning includes problem-based learning, and is generally used in small scale investigations and projects, as well as research. The inquiry-based instruction is principally very closely related to the development and practice of thinking and problem solving skills.

**Floyd Grant Robinson** is a teacher, education theorist and curriculum developer. He has written many works on the topics of stimulating complex thinking and the importance of education across the entire lifespan. Robinson is most notable for his work done while at the Ontario Institute for Studies in Education (OISE) between 1965 and 1991.

**Thematic teaching** is the selecting and highlighting of a theme through an instructional unit or module, course, or multiple courses. It is often interdisciplinary, highlighting the relationship of knowledge across academic disciplines and everyday life. Themes can be topics or take the form of overarching questions. Thematic learning is closely related to interdisciplinary or integrated instruction, topic-, project- or phenomenon-based learning. Thematic teaching is commonly associated with elementary classrooms and middle schools using a team-based approach, but this pedagogy is equally relevant in secondary schools and with adult learners. A common application is that of second or foreign language teaching, where the approach is more commonly known as theme-based instruction. Thematic instruction assumes students learn best when they can associate new information holistically with across the entire curriculum and with their own lives, experiences, and communities.

**Embodied design** grows from the idea of embodied cognition: that the actions of the body can play a role in the development of thought and ideas. Embodied design brings mathematics to life; studying the effects of the body on the mind, researchers learn how to design objects and activities for learning. Embodiment is an aspect of pattern recognition in all fields of human endeavor.

- 1 2 3 4 Van de Walle, John A. (April 1, 2003). "Reform Mathematics vs. The Basics: Understanding the Conflict and Dealing with It". Mathematically Sane.
- ↑ "John Van de Walle Biography". National Council of Teachers of Mathematics. Retrieved 21 September 2014.
- 1 2 3 4 "Sketch of a Three-Part Lesson". Ontario College of Teachers. March 2010.
- ↑ Small, Marian (2012). "How Students Learn Math and What Math We Want Them to Learn" (PDF). Cengage Learning.
- 1 2 Alphonso, Caroline; Morrow, Adrian (August 28, 2013). "Ontario Teachers Need Better Math Training, Minister Says". Globe and Mail.

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