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

**Inquiry-based learning** is a form of active learning that starts by posing questions, problems or scenarios—rather than simply presenting established facts or portraying a smooth path to knowledge. The process is often assisted by a facilitator. Inquirers will identify and research issues and questions to develop their 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 skills.

- 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] }

**Virginia Commonwealth University** (**VCU**) is a public research university located in Richmond, Virginia. MCV was founded in 1838 as the medical department of Hampden–Sydney College, becoming the Medical College of Virginia in 1854. In 1968, the Virginia General Assembly merged MCV with the Richmond Professional Institute, founded in 1917, to create Virginia Commonwealth University. In 2018, more than 31,000 students pursue 217 degree and certificate programs through VCU's 11 schools and three colleges. The VCU Health System supports the university's health care education, research and patient care mission.

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] }

**Marian Small** is a Canadian educational researcher, academic, author, and public speaker. She has co-authored mathematics textbooks used in Canada, Austria, and the United States, and is a proponent of a constructivist approach to mathematical instruction within K–12 classrooms.

**Constructivist teaching** is based on constructivist learning theory. Constructivist teaching is based on the belief that learning occurs as learners are actively involved in a process of meaning and knowledge construction as opposed to passively receiving information. Learners are the makers of meaning and knowledge.

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 a lot of 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. The PBL process was developed for medical education and has since been broadened in applications for other programs of learning. The process allows for learners to develop skills used for their future practice. It enhances critical appraisal, literature retrieval and encourages ongoing learning within a team environment.

**Constructivism** is a philosophical viewpoint about the nature of knowledge. Therefore, it represents an epistemological stance.

* Principles and Standards for School Mathematics* (

The **National Council of Teachers of Mathematics** (**NCTM**) was founded in 1920. It provides services concerning mathematics education in the United States and Canada.

**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.

**Cognitive apprenticeship** is a theory that emphasizes the importance of the process in which a master of a skill teaches that skill to an apprentice.

**Saxon math**, developed by John Saxon, is a teaching method for incremental learning of mathematics. 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. Its primary strength is in a steady review of all previous material, which is especially important to students who struggle with retaining the math they previously learned.

**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. Although this form of instruction has great popularity, there is some debate in the literature concerning its efficacy.

**Formative assessment**, 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. 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.

**Traditional mathematics** was the predominant method of mathematics education in the United States in the early-to-mid 20th century. This contrasts with non-traditional approaches to math education. Traditional mathematics education has been challenged by several reform movements over the last several decades, notably new math, a now largely abandoned and discredited set of alternative methods, and most recently reform or standards-based mathematics based on NCTM standards, which is federally supported and has been widely adopted, but subject to ongoing criticism.

**Investigations in Numbers, Data, and Space** is a K–5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, United States. The curriculum is often referred to as *Investigations* or simply *TERC*. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. As opposed to referring to textbooks and having teachers impose methods for solving arithmetic problems, the TERC program uses a constructivist approach that encourages students to develop their own understanding of mathematics. The curriculum underwent a major revision in 2005–2007.

**Basic skills** can be compared to higher order thinking skills. Facts and methods are highly valued under the back-to-basics approach to education.

**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.

**Singapore math** is a teaching method based on the national mathematics curriculum used for kindergarten through sixth grade in Singapore. 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 concrete objects such as chips, dice, or paper clips. 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.

**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 September 2014.Check date values in:
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(help) - 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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