Understanding exists along a continuum (Figure 1.3) from an instrumental understanding— knowing something by rote or without meaning (Skemp, 1978)—to a relational understanding— knowing what to do and why.

What is instrumental understanding and relational understanding?

Instrumental understanding – having a mathematical rule and being able to apply and manipulate it. Relational understanding – having a mathematical rule, knowing how to use it AND knowing why it works.

What is the difference between instrumental and relational mathematics?

Instrumental mathematics centre around rote learning, memory, rules and correct answers. Relational mathematics focus more on establishing connections, building understanding over time, applying concepts to other problems, and gradual increases in complexity.

What does relational understanding mean?

Relational understanding means investigating concepts along a continuum, integrating related concepts, and could be described as ‘owning your maths’! Relational or Instrumental Understanding Video. Richard Skemp believed that children could learn intelligently from a young age.

What does relational understanding can be linked to?

Relational understanding refers to knowing both what to do and why – an understanding of all of the parts, how they relate, and why they are applied in the manner they are.

What is teaching for instrumental understanding?

“Instrumental understanding” can be thought of as knowing the rules and procedures without understanding why those rules or procedures work. … Students who are taught instrumentally come to see mathematics as isolated pieces of knowledge. They are expected to remember procedures for each and every concept/skill.

How do you develop relational understanding?

Growing relational understanding requires time, but relational understanding is able to develop four things including (1) developing a correct understanding of mathematical concepts; (2) training students to normally see the problem as a whole; (3) developing skills in using mathematical principles and concepts; (4) …

What is relational thinking in math?

Relational thinking mostly concerns examining the relations between the given quantities rather than finding the result of operations. To clarify, relational thinking involves use of fundamental properties of numbers and operations for the transformation of mathematical sentences.

How can relational understanding promote reflective thinking?

Relational understanding allows people to have a more reflective attitude to learning and allows for more exploration to occur. From this, I can see that relational understanding is a deeper, more complex understanding of instrumental understanding.

How can understanding be defined in mathematics?

Understanding refers to a student’s grasp of fundamental mathematical ideas. Students with understanding know more than isolated facts and procedures. They know why a mathematical idea is important and the contexts in which it is useful. … For example, students who understand division of fractions not only can compute .

Article first time published on

What is the difference between procedural and conceptual understanding?

Procedural understanding is when students hoard steps and algorithms. … Conceptual understanding is knowing the procedural steps to solving a problem and understanding why those algorithms and approaches work, similar to a recognition that there is a man hiding behind the giant head in The Wizard of Oz.

Has been instrumental meaning?

If someone or something is instrumental in a process, plan, or system, that person or thing is one of the most important influences in causing it to happen: She was instrumental in bringing about the prison reform act. SMART Vocabulary: related words and phrases.

What is Zoltan Dienes theory?

A Hungarian-born mathematician and theorist, Zoltan Dienes believed in using games, songs and dance in learning math to make it more fun for children. … His theory was that by using manipulative materials, games and stories, children can learn more complicated math at a younger age than had previously been thought.

Why is conceptual understanding important?

Conceptual understanding, where children can grasp ideas in a transferrable way, can help students take what they learn in class and apply it across domains. … They learned best when they saw examples of solutions rather than being given an explicit rule.

What does creating opportunities for reflective thought mean?

Reflective thought and action is encouraged by questioning techniques that enable students to articulate their thinking. This includes encouraging metacognition as well as building on students’ responses by rephrasing, adding and inviting further responses from other students.

What are some examples of learning strategies?

  • Spaced Practice. Space out your studying over time. …
  • Retrieval Practice. Practice bringing information to mind without the help of materials. …
  • Elaboration. Explain and describe ideas with many details. …
  • Interleaving. Switch between ideas while you study. …
  • Concrete Examples. …
  • Dual Coding.

What does the relational understanding of place value begin with?

Money. What does the relational understanding of place value begin with? Counting by ones, making a model and saying and writing the numeral.

Is Mathematize a word?

verb (used with object), math·e·ma·tized, math·e·ma·tiz·ing. to reduce to a mathematical formula or problem; regard in purely mathematical terms.

What is conceptual and procedural knowledge?

Conceptual knowledge is the result of a student successfully acquiring conceptual understanding. Procedural knowledge is the result of a student successfully learning a procedure.

What is your understanding of a learning strategy?

A learning strategy is an individual’s way of organizing and using a particular set of skills in order to learn content or accomplish other tasks more effectively and efficiently in school as well as in non-academic settings (Schumaker & Deshler, 1992).

What is the purpose of mathematics teaching in FET phase?

Purpose: The purpose of this module is to ensure that qualifying student teachers: – acquire the knowledge, skills, values and attitudes that will enable them to teach Mathematics in FET; – integrate knowledge and skills acquired from other modules in the qualification such as Instructional studies, Curriculum …

What is reflective thinking?

Critical thinking and reflective thinking are often used synonymously. … Dewey (1933) suggests that reflective thinking is an active, persistent, and careful consideration of a belief or supposed form of knowledge, of the grounds that support that knowledge, and the further conclusions to which that knowledge leads.

Why might skemp's ideas be important for teachers of primary mathematics?

Despite his preference of relational understanding, Skemp proposes three advantages of instrumental mathematics that make it preferred amongst many mathematics teachers: (a) within its own context, instrumental mathematics is often easier to understand; (b) the rewards for following a procedure and getting a correct …

What is comparative relational thinking?

Use comparative relational thinking to look and see how the addends on one side of the equation relate to those on the other side. … This method will also work for an equation involving subtraction. With a subtraction problem, you must add or subtract the same number to both number pairs on each side of the equation.

What is the difference between algebraic thinking and arithmetic thinking?

(A) Arithmetic is about computation of specific numbers. Algebra is about what is true in general for all numbers, all whole numbers, all integers, etc. Going from the specific to the general is a giant conceptual leap.

How does algebraic thinking differ from arithmetic thinking?

Every thing is based on it, arithmetic consists of simple operations like division, multiplication, addition and subtraction, where as algebra is the math of finding unknown values in an equation with the help of variables(variables are symbols that represent an unknown value).

How do you show conceptual understanding in math?

  1. Belief. Leah Alcala has the utmost belief that her students will be able to access and attempt the task at hand. …
  2. Sense Making. …
  3. Scaffolding. …
  4. Time. …
  5. Multiple Representations.

What is an example of conceptual understanding in mathematics?

For example, many children learn a routine of “borrow and regroup” for multi-digit subtraction problems. Conceptual knowledge refers to an understanding of meaning; knowing that multiplying two negative numbers yields a positive result is not the same thing as understanding why it is true.

How do students show conceptual understanding in math?

One way that students can demonstrate conceptual understanding is by solving a math problem while articulating what they are doing. When students explain their thinking about a math problem, it gives the teacher insight into a student’s metacognitive thinking and ability to use math language.

What is a conceptual understanding?

Conceptual understanding refers to an integrated and functional grasp of mathematical ideas. Students with conceptual understanding know more than isolated facts and methods. They understand why a mathematical idea is important and the kinds of contexts in which is it useful.

What is conceptual understanding in mathematics PDF?

While procedural understanding focusses on performing facts and algorithms, conceptual understanding reflects a student’s ability to reason and comprehend mathematical concepts, operations and relations which will be helpful in solving non-routine problems.