583 0 obj 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. H��WKo#7��Wp/Aw�f��wd1�'��f�Ƹ�<9�����li�~H3� �.��$6�&�U_}��i}�x���,W;�����n�Z�����~+~�OO��0�0�L�,YjdZe�� What should a classroom look like if teachers are helping students build conceptual understanding in mathematics? endobj One article that I found on the subject procedural fluency concerns practicing frequent mental math in the classroom (link: Burns, M. K., Walick, C., Simonson, G. R., Dominguez, L., Harelstad, L., Kincaid, A., &. <>]/P 570 0 R/Pg 874 0 R/S/Reference>> endobj endobj These key components help to guide the aim of this paper, by providing an <> endobj Although mental math may not be exactly procedural fluency, it does help in building it. It helped me to realize not only what procedural fluency is, but how important it is in the mathematics classroom. Understanding makes learning skills easier, less susceptible to common errors, and less prone to forgetting. <> 577 0 obj A teacher-driven, rather than student-driven, approach to instruction was emphasized, thus minimizing opportunities for students to engage in the kinds of tasks and discourse recommended in the literature. Change ), The effective mathematics teaching practice that I was assigned to read about from, was building procedural fluency from conceptual understanding. This can be done through encouraging students to look at different ways to approach problems, connecting the mathematics learned to real world applications, and focusing on group work after students have had the opportunity to approach a problem individually. “Effective teaching of mathematics builds fl uency with pro-cedures on a foundation of conceptual understanding so that students, over time, become skillful in using proce-dures fl exibly as they solve contextual and mathematical problems” (italics added) (NCTM 2014a, p. 10). for building procedural fluency from conceptual understanding can be found in the table below. <> <>]/P 572 0 R/Pg 874 0 R/S/Reference>> Number talks provide a brief, daily opportunity for students to discuss, connect and develop their strategies for solving problems. endobj REGISTRATION CLOSED – Build Procedural Fluency from Conceptual Understanding – Session. endobj The ways Please watch, like and subscribe my channel. endobj Learning Disabilities Research & Practice (Wiley-Blackwell). <>]/P 560 0 R/Pg 874 0 R/S/Reference>> <>]/P 574 0 R/Pg 874 0 R/S/Reference>> endobj 870 0 obj 555 0 obj Conceptual understanding and procedural fluency are equally important. <>]/P 568 0 R/Pg 874 0 R/S/Reference>> <>]/P 564 0 R/Pg 874 0 R/S/Reference>> In order to enhance CU and PF, students need learning experiences in constructing knowledge I identified a priori codes, and allowed for emergent codes, that characterize quality mathematical instruction. I would like to implement no calculator quizzes and exams (not all) in my future classroom to help students build a procedural fluency in their mental mathematics. Strategies and Tasks to Build Procedural Fluency from Conceptual Understanding Diane J. Briars Immediate Past President National Council of Teachers of Mathematics dbriars@nctm.org @dbriars 2016 NCTM Phoenix Regional Conference October 27, 2016 589 0 obj <>]/P 554 0 R/Pg 874 0 R/S/Reference>> <>]/P 584 0 R/Pg 874 0 R/S/Reference>> 616 0 obj Procedural fluency aids in problem solving skills, which are at the heart of mathematics. ( Log Out /  Reading about building procedural fluency through conceptual understanding prompted me to reflect on my own procedural fluency, and how I can build procedural fluency in my future students. <> 505 0 obj Like all of us, students have finite energy. Another article that I found was a study done in an elementary school involving utilizing a conceptual understanding versus procedural fluency. endobj 624 0 obj Reading this article, I began to reflect on my own use of mental math since beginning college. <>]/P 586 0 R/Pg 874 0 R/S/Reference>> endobj endobj Analyze a problem Teacher & Student Actions Questions & Closing. They are both part of five strands that define math proficiency according to the National Research Council. <>]/P 556 0 R/Pg 874 0 R/S/Reference>> Nelson, G. S. (2015). endobj <>]/P 612 0 R/Pg 898 0 R/S/Reference>> endobj <>]/P 625 0 R/Pg 907 0 R/S/Reference>> My first college course was Honors Calc II, and no calculators were allowed. <> endobj <>]/P 608 0 R/Pg 898 0 R/S/Reference>> ... procedural fluency from conceptual understanding. Build procedural fluency from conceptual understanding. [915 0 R] <>]/P 540 0 R/Pg 872 0 R/S/Reference>> 1 0 obj If a student doesn’t have a strong conceptual understanding of a concept then, their ability to build procedural fluency with the algorithm will be limited. Build Procedural Fluency from Conceptual Understanding Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems. 599 0 obj 553 0 obj They split students into two groups, keeping track of previous ability in mathematics, and administer a conceptual understanding intervention to one group and a procedural fluency intervention to the other group. endobj <>stream 607 0 obj <>]/P 580 0 R/Pg 874 0 R/S/Reference>> “ Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so … The National Council of Teachers of Mathematics state the “effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems” (Principles to Actions: Ensuring Mathematical Success for All, p. 42). <>/Font<>>>/Rotate 0/StructParents 98/Type/Page>> Build procedural fluency from conceptual understanding. These students did not have a conceptual understanding of how to perform multiplication, addition, subtraction, or division, thus hindering their procedural fluency. What is Conceptual Understanding, Procedural Fluency and Mathematical Reasoning/Problem Solving? In reality, a handful of good problems allows students to practice and build their understanding of new concepts. endobj They also point out that students also need to develop productive dispositions, the ability to reason logically and be able to formulate, represent and solve mathematical problems. 585 0 obj endobj 575 0 obj 2 0 obj <><>]/P 623 0 R/Pg 907 0 R/S/Reference>> Build Procedural Fluency from Conceptual Understanding part of The Effective Mathematics Teaching Practices series In 2014, the National Council of Teachers of Mathematics (NCTM) published Principles to Action. endobj 3 0 obj <> 609 0 obj I can use the information found in this article, and others to help my future students learn procedural fluency in the math that they encounter. <>]/P 582 0 R/Pg 874 0 R/S/Reference>> <> Elicit and use evidence of student thinking. (2015). <>]/P 566 0 R/Pg 874 0 R/S/Reference>> 565 0 obj Furthermore, in my internship last fall, I found that the majority of students in the sixth grade classroom that I had the opportunity to observe still used a multiplication table, and were unable to perform the calculations on their own. endobj 21). endobj This is not an infinite set of problems that students must complete in a finite time period. These practices include a call to build procedural fluency from conceptual understanding, stating that “Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skilful in using procedures Five keys for teaching mental math. 551 0 obj CU helps students organizing their knowledge into a coherent whole, and PF helps them to find the right solution of a problem. Meaningful practice is necessary to develop fluency with basic number combinations and … <>]/P 610 0 R/Pg 898 0 R/S/Reference>> <>]/P 596 0 R/Pg 874 0 R/S/Reference>> endobj Now I see that conceptual understanding and procedural fluency can be developed together. The following table shows what we should expect teachers to be doing and what we should expect students to be doing to build procedural fluency from conceptual understanding (adapted from NCTM's Principles to Actions: Ensuring Mathematical Success for All, p. 47-48). 12 As we noted earlier, the two are interwoven. This was a stark difference from my high school classroom where calculators were heavily relied upon. Agenda Revisit the Math Shifts Discussion on responses to pre-reading What is procedural fluency & how do you build it? ( Log Out /  <>]/P 592 0 R/Pg 874 0 R/S/Reference>> endobj �U�.�׻��Vį�e�>�������]���������3q�]*�zJ��Uw׵Z�7'�����L)�4�Fԛ��2a���v��*�4�R5Z-pq�%���F�n���7h������s���PR��������� 591 0 obj But pitting skill against understanding creates a false dichotomy. endobj Thank you for watching my channel. <>]/P 590 0 R/Pg 874 0 R/S/Reference>> (Remember: conceptual understanding , procedural skills and fluency , and application are the three aspects of rigor , a key shift called for by the Common Core.) <>]/P 588 0 R/Pg 874 0 R/S/Reference>> The idea is that teachers should strive to build this procedural fluency in their students from the conceptual understanding that the students have through making connections between concepts, or introducing multiple ways to approach a problem. Learning Disabilities Research & Practice (Wiley-Blackwell), 30(2), 52-60. doi:10.1111/ldrp.12056. <>]/P 562 0 R/Pg 874 0 R/S/Reference>> 561 0 obj endobj <> 581 0 obj This can be done through encouraging students to look at different ways to approach problems, connecting the mathematics learned to real world applications, and focusing on group work after students have had the opportunity to approach a problem individually. Prince 9.0 rev 5 (www.princexml.com) Conceptual understanding in itself is a functional understanding of concepts, operations, and relations presented in the mathematics classroom, whereas procedural fluency is the ability to execute procedures accurately, efficiently, and flexibly. endobj endobj Each perspective will build off each other to form a comprehensive view of learning and teaching algebra. K-8 (HMH, 2016) supports teachers in building procedural fluency from conceptual understanding when teaching equivalence of fractions.Krippendorf<'>s (1980) framework for content analysis guided this study. The results of this study are indicative of what I should remember in my future classroom: that my students must understand the material fully before they will be able to build procedural fluency. endobj The idea is that teachers should strive to build this procedural fluency in their students from the conceptual understanding that the students have through making connections between concepts, or introducing multiple ways to approach a problem. <>stream It helped me to realize not only what procedural fluency is, but how important it is in the mathematics classroom. Procedural fluency aids in problem solving skills, which are at the heart of mathematics. 573 0 obj lesson” (NCTM, 2014). (2015). This idea aligns with standard 7.SP.5. endobj <>]/P 600 0 R/Pg 898 0 R/S/Reference>> The suggestions made in Principles to Actions for building procedural fluency from conceptual understanding can be found in the table below. 618 0 obj <>]/P 552 0 R/Pg 874 0 R/S/Reference>> <><>]/P 615 0 R/Pg 907 0 R/S/Reference>> Students must develop conceptual understanding of mathematics as well as procedural fluency. Change ), You are commenting using your Google account. The latest round of curriculum reforms is wrapped in the language of balance between procedural fluency and conceptual understanding. In the article ‘A Distinction Between Conceptual Knowledge and Procedural Knowledge‘ J. E. Schwartz writes poignantly about the difference between conceptual knowledge and procedural knowledge, how math education has historically focused on the latter, and how having procedural knowledge without conceptual knowledge thwarts a person’s mathematical development. 6 0 obj From the Common Core State Standards: Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. The New York State Mathematics Core Curriculum is broken down into three main components: conceptual understanding, procedural fluency, and problem solving. Change ), You are commenting using your Facebook account. You must be logged in to post a comment. endobj endobj endobj endobj uuid:eb281bce-ab94-11b2-0a00-782dad000000 endobj Procedural fluency is especially needed to support conceptual understanding of place value and the meanings of … <>]/P 621 0 R/Pg 907 0 R/S/Reference>> endobj 2019-05-23T23:36:52-07:00 502 0 obj Conceptual understanding (CU) and procedural fluency (PF) are two important mathematical competencies required by students. The way that I think of mental math may be different from another student, and there are different ways to approach each problem. Inspiring and Leading through Excellence in Education. 504 0 obj <>]/P 431 0 R/Pg 916 0 R/S/Link>> While students may understand a concept, they may not be able to apply it to another problem. National Council of Teachers of Mathematics (2014). 563 0 obj Meaningful independent practice builds conceptual understanding and procedural fluency. <> Procedural fluency and conceptual understanding are often seen as competing for attention in school mathematics. As a result, it is essential for educators to support students in developing both abilities. endobj Procedural Fluency from Conceptual Understanding. uuid:eb28a275-ab94-11b2-0a00-c0d1b05afc7f What this looks like in the classroom is a student who constantly makes errors in place value when multiplying multi-digit numbers. 567 0 obj Effective Mathematics Teaching Principles, http://www.nctm.org/Publications/Mathematics-Teacher/2015/Vol108/Issue7/Five-Keys-for-Teaching-Mental-Math/. 13 0 obj The effective mathematics teaching practice that I was assigned to read about from Principles to Actions was building procedural fluency from conceptual understanding. AppendPDF Pro 5.5 Linux Kernel 2.6 64bit Oct 2 2014 Library 10.1.0 ( Log Out /  Connect conceptual understanding with procedural fluency to provide students with a wider range of options for entering a task and building mathematical meaning. 916 0 obj With strong Common Core instruction, students are supported to develop conceptual understanding alongside the procedural skills and fluencies: they understand why the algorithm works. Conceptual understanding in itself is a functional understanding of concepts, operations, and relations presented in the mathematics classroom, whereas procedural fluency is the ability to execute procedures accurately, efficiently, and flexibly. An infinite set of problems that students must complete in a finite time.! Teachers are helping students build conceptual understanding in mathematics makes learning skills easier, less susceptible to common errors and. Errors in place value and the meanings of … lesson ” ( NCTM, 2014 ) the that. 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And teaching algebra the heart of mathematics icon to Log in: You are commenting using your Google.... Reasoning/Problem solving allows students to discuss, connect and develop their strategies solving... Errors in place value and the meanings of … lesson ” (,... This that conceptual understanding in mathematics intervention better, i.e aids in problem solving skills, which are at heart.

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