{"id":3206,"date":"2025-11-04T11:13:40","date_gmt":"2025-11-04T19:13:40","guid":{"rendered":"https:\/\/theothermath.com\/?p=3206"},"modified":"2025-11-04T11:13:40","modified_gmt":"2025-11-04T19:13:40","slug":"the-importance-of-math-fluency-and-how-to-achieve-it","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2025\/11\/04\/the-importance-of-math-fluency-and-how-to-achieve-it\/","title":{"rendered":"The Importance of Math Fluency and How to Achieve It"},"content":{"rendered":"<p class=\"c8\"><span class=\"c3\">The other day I received a text from a school district I serve. It read, &#8220;On a scale of 1-10, how important is math fact fluency?&#8221;<\/span><\/p>\n<p class=\"c8\"><span class=\"c3\">My answer: \u00a011<\/span><\/p>\n<p class=\"c8\"><span class=\"c3\">In a follow-up text, they asked for my thoughts on fluency instruction, fluency practice, and whether there are any online apps to support the development of fluency. I thought I&#8217;d share my thoughts for all to read.<\/span><\/p>\n<p class=\"c8\"><span class=\"c3\">Here we go\u2026<\/span><\/p>\n<p class=\"c8\"><span class=\"c3\">There are a bazillion online apps claiming to develop fluency, but first let&#8217;s describe what \u2013 exactly \u2013 fluency is.<\/span><\/p>\n<p class=\"c8\"><span class=\"c3\">For most people, math fact fluency means the quick and accurate recall of basic math facts in addition, subtraction, multiplication, and division. This is a correct, but incomplete, definition of fact fluency.<\/span><\/p>\n<h1 id=\"h.hwcgd5lrq3r2\" class=\"c25\"><span class=\"c9 c17\">What is basic math fact fluency?<\/span><\/h1>\n<p class=\"c8\">Basic math fact fluency requires the presence of\u00a0<span class=\"c14 c22\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/nwcommons.nwciowa.edu\/cgi\/viewcontent.cgi?article%3D1516%26context%3Deducation_masters&amp;sa=D&amp;source=editors&amp;ust=1762286597657600&amp;usg=AOvVaw0l24Gr7ZqQh8RitMiGrL-1\">FOUR critical components<\/a><\/span><span class=\"c3\">:<\/span><\/p>\n<ul>\n<li class=\"c8\"><span class=\"c3\">Efficiency<\/span><\/li>\n<li class=\"c8\"><span class=\"c3\">Accuracy<\/span><\/li>\n<li class=\"c8\"><span class=\"c3\">Flexibility<\/span><\/li>\n<li class=\"c8\"><span class=\"c3\">Appropriate choice of strategy<\/span><\/li>\n<\/ul>\n<p class=\"c8\"><span class=\"c3\">For decades we have focused on the first two components \u2013 efficiency (fast) and accuracy \u2013 while underdeveloping our students&#8217; ability to think flexibly about the numbers and select an appropriate strategy for arriving at the answer if the answer does not immediately come to mind.<\/span><\/p>\n<p class=\"c8\">When we use this broader vision of math fact fluency, it suddenly calls into question our use of flashcards and online apps that merely provide some sort of naked problem (like 6 x 8) and feedback based on the student&#8217;s answer (happy bells for correct answers and buzzers for wrong answers). This is because flashcards and most online apps only focus on speed and accuracy, while completely ignoring flexibility and appropriate choice of strategy.<\/p>\n<h1 id=\"h.u35eyfu7ts5b\" class=\"c20\"><span class=\"c9 c17\">The secret to developing fact fluency<\/span><\/h1>\n<p class=\"c5\"><span class=\"c1\">Lemme put it simply: Students using a\u00a0<\/span><span class=\"c1 c15\">strategy-based approach\u00a0<\/span><span class=\"c1\">for fluency development by means of instructional tasks emphasizing strategies and conceptual understanding increase fact fluency, with a greater degree of consistency, than students using a\u00a0<\/span><span class=\"c1 c15\">drill-based approach\u00a0<\/span><span class=\"c9 c1\">emphasizing repetition and memorization.<\/span><\/p>\n<p class=\"c5\"><span class=\"c9 c1\">How do I know? Here are two PDFs that I&#8217;m drawing upon:<\/span><\/p>\n<p class=\"c5\"><span class=\"c9 c1\">This PDF is general and includes discussion about both addition AND multiplication facts.<\/span><\/p>\n<p class=\"c5\"><span class=\"c14 c1\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/drive.google.com\/file\/d\/1A_VRYvyBex_GIV9hgEFw9zM40E74FXe-\/view?usp%3Ddrive_link&amp;sa=D&amp;source=editors&amp;ust=1762286597661793&amp;usg=AOvVaw24rpbiORclI5vkqxo6bDch\">https:\/\/drive.google.com\/file\/d\/1A_VRYvyBex_GIV9hgEFw9zM40E74FXe-\/view?usp=drive_link<\/a><\/span><\/p>\n<p>&nbsp;<\/p>\n<p class=\"c5\"><span class=\"c9 c1\">This PDF is specific to multiplication.<\/span><\/p>\n<p class=\"c5\"><span class=\"c14 c1\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/drive.google.com\/file\/d\/1kXQpWyqg8awl3wHPyafg4LgOBuvNqGv8\/view?usp%3Dsharing&amp;sa=D&amp;source=editors&amp;ust=1762286597662439&amp;usg=AOvVaw0nEm0hQvjAyWdADyhnKLw2\">https:\/\/drive.google.com\/file\/d\/1kXQpWyqg8awl3wHPyafg4LgOBuvNqGv8\/view?usp=sharing<\/a><\/span><\/p>\n<p class=\"c5\"><span class=\"c9 c1\">At little less formal than the two prior resources, here is a nice article that I use in my training:<\/span><\/p>\n<p class=\"c5\"><span class=\"c1 c14\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.edutopia.org\/article\/how-decreased-practice-time-plays-into-historic-math-declines\/&amp;sa=D&amp;source=editors&amp;ust=1762286597663184&amp;usg=AOvVaw1d1thsFhPL1lBhaLrZvlnB\">https:\/\/www.edutopia.org\/article\/how-decreased-practice-time-plays-into-historic-math-declines\/<\/a><\/span><\/p>\n<h1 id=\"h.sq4f9u3rwlnc\" class=\"c25\"><span class=\"c9 c17\">How do we develop math fact fluency?<\/span><\/h1>\n<p class=\"c5\"><span class=\"c1\">In general, we all agree on the WHAT: students need to be fluent with math facts.<\/span><span class=\"c7\">\u00a0<\/span><\/p>\n<p class=\"c5\"><span class=\"c1\">It is the HOW, however, that gets sticky. Students need to be taught how to visualize the numbers and also need to be taught specific strategies for &#8220;getting the answer&#8221; that will eventually lead to procedural fluency and automaticity. Using drill-and-kill software that focuses merely on memorization without including a huge emphasis on conceptual understanding and strategies is likely to be a waste of everyone&#8217;s time.<\/span><\/p>\n<p class=\"c8\"><span class=\"c7\">We develop math fact fluency by guiding students through three stages in order:<\/span><\/p>\n<h2 id=\"h.76jco04oeise\" class=\"c12\"><span class=\"c9 c21\">Stage 1: Conceptual Learning<\/span><\/h2>\n<p class=\"c8\"><span class=\"c7\">We begin by teaching the meaning of the operations so students truly understand them. Students in early grades begin by understanding that addition and subtraction mean join together and take apart. In third and fourth grade students need to learn that multiplication and division means joining and separating equal groups. To reinforce the meanings of each operation, students must be given ample opportunities to use lots of concrete manipulatives and pictorial models.<\/span><\/p>\n<p class=\"c8\"><span class=\"c7\">\u00a0<\/span><\/p>\n<h2 id=\"h.in27xzk9ox9l\" class=\"c12\"><span class=\"c9 c21\">Stage 2: Learn Fact Strategies<\/span><\/h2>\n<p class=\"c8\"><span class=\"c16\">Rather than merely focusing on memorization of facts, teachers need to explicitly teach strategies for deriving answers. For\u00a0<\/span><span class=\"c14 c16\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2025\/10\/27\/how-to-teach-addition-facts\/&amp;sa=D&amp;source=editors&amp;ust=1762286597667419&amp;usg=AOvVaw2giQideFNLuW-7Y816rraq\">addition and subtraction<\/a><\/span><span class=\"c16\">,<\/span><span class=\"c16\">\u00a0examples of these strategies are make a ten, doubles, add a friendly number, etc. In\u00a0<\/span><span class=\"c14 c16\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2024\/11\/05\/how-to-teacher-the-multiplication-facts\/&amp;sa=D&amp;source=editors&amp;ust=1762286597667878&amp;usg=AOvVaw1NuSoCPUW9c79pia152I1l\">multiplication and division<\/a><\/span><span class=\"c7\">\u00a0strategies might include doubling and halving, distributive property, multiply by a friendly number, etc.<\/span><\/p>\n<p class=\"c8\"><span class=\"c7\">Students need to be provided with lots of opportunities to practice and apply these strategies, while emphasizing relationships and connections between the numbers and recognizing which strategy is more efficient than the others. Students are still expected to use lots of manipulatives and models, but now it is to develop deeper insight as to WHY the strategies work and to justify why they used a particular strategy.<\/span><\/p>\n<p class=\"c8\"><span class=\"c7\">\u00a0<\/span><\/p>\n<h2 id=\"h.xq495hmbma0a\" class=\"c12\"><span class=\"c9 c21\">Stage 3: Memorization of Basic Math Facts<\/span><\/h2>\n<p class=\"c8\"><span class=\"c16\">Students are finally ready to begin putting their facts to memory through a variety of practice. This might be in the form of games,\u00a0<\/span><span class=\"c14 c16\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2023\/12\/10\/learning-multiplication-with-flashcards\/&amp;sa=D&amp;source=editors&amp;ust=1762286597669997&amp;usg=AOvVaw1MYtoLEapVNRXeVz6hSls1\">flashcards<\/a><\/span><span class=\"c16\">, online applications, etc. Whatever form of practice you choose for your students, keep it fun! Your target is for students to recall a fact within 2 to 3 seconds. Ideally, students will be given math facts to remember through an approach called\u00a0<\/span><span class=\"c14 c22 c23\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/en.wikipedia.org\/wiki\/Spaced_repetition&amp;sa=D&amp;source=editors&amp;ust=1762286597670536&amp;usg=AOvVaw0x8l4pJy8jMemHYMQ5l6L2\">spaced repetition<\/a><\/span><span class=\"c7\">, in which students are shown facts they are most likely to forget thereby ensuring all problems reach long-term memory.<\/span><\/p>\n<p class=\"c8\"><span class=\"c7\">By the time students have reached Stage 3, many of the facts will already be in long-term memory simply through the repeated efforts of Stage 1 and Stage 2. Essentially, students are REMEMBERING their facts more than they are MEMORIZING them.<\/span><\/p>\n<h1 id=\"h.es19mup1x97y\" class=\"c20\"><span class=\"c9 c17\">What might this look like in an after-school setting?<\/span><\/h1>\n<p class=\"c5\"><span class=\"c9 c1\">Teachers need to do stages 1, 2, and 3 within their classrooms. Perhaps flashcards can assigned as homework\u2026assuming both students AND parents are clear that the purpose of the flashcards is to build understanding and not necessarily speed.<\/span><\/p>\n<p class=\"c5\"><span class=\"c9 c1\">Invariably, however, you will also need to consider some sort of extended learning opportunity with the math facts. What might this look like in an after-school setting?<\/span><\/p>\n<ul class=\"c2 lst-kix_igm2y7pjfipi-0 start\">\n<li class=\"c5 c13 li-bullet-0\"><span class=\"c9 c1\">An adult might work with a small group of students to provide direct instruction on specific addition and\/or multiplication strategies.<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-1 start\">\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c1\">Addition strategies\u00a0<\/span><span class=\"c6\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2025\/10\/27\/how-to-teach-addition-facts\/&amp;sa=D&amp;source=editors&amp;ust=1762286597673525&amp;usg=AOvVaw1Xs6C-S0Ye0FO2G4M-wcvE\">(Here is a blog I wrote)<\/a><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-2 start\">\n<li class=\"c0 li-bullet-0\"><span class=\"c9 c1\">Count on by 1 or 2<\/span><\/li>\n<li class=\"c0 li-bullet-0\"><span class=\"c9 c1\">Make a ten<\/span><\/li>\n<li class=\"c0 li-bullet-0\"><span class=\"c9 c1\">Doubles and near doubles<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-1\">\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c1\">Multiplication strategies \u00a0<\/span><span class=\"c6\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2024\/11\/05\/how-to-teacher-the-multiplication-facts\/&amp;sa=D&amp;source=editors&amp;ust=1762286597674135&amp;usg=AOvVaw272LQTn4ubVdaMKfD6Ty1L\">(Blog post 1)<\/a><\/span><span class=\"c22 c24\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2024\/11\/05\/how-to-teacher-the-multiplication-facts\/&amp;sa=D&amp;source=editors&amp;ust=1762286597674271&amp;usg=AOvVaw3kVG_i6mKU6z0P1q9V6Osg\">\u00a0<\/a><\/span><span class=\"c1\">\u00a0\u00a0<\/span><span class=\"c6\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/2023\/12\/10\/learning-multiplication-with-flashcards\/&amp;sa=D&amp;source=editors&amp;ust=1762286597674493&amp;usg=AOvVaw2vMrCaMDo2-N18vQGfKcNL\">(Blog post 2)<\/a><\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-2 start\">\n<li class=\"c0 li-bullet-0\"><span class=\"c9 c1\">Adding or subtracting a group<\/span><\/li>\n<li class=\"c0 li-bullet-0\"><span class=\"c9 c1\">Halving and doubling<\/span><\/li>\n<li class=\"c0 li-bullet-0\"><span class=\"c9 c1\">Decomposing a factor<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul class=\"c2 lst-kix_igm2y7pjfipi-0\">\n<li class=\"c5 c13 li-bullet-0\"><span class=\"c9 c1\">Concrete manipulatives are used to support number sense.<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-1 start\">\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">Ten frames<\/span><\/li>\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">Number lines<\/span><\/li>\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">Numicon<\/span><\/li>\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">Grid paper<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul class=\"c2 lst-kix_igm2y7pjfipi-0\">\n<li class=\"c5 c13 li-bullet-0\"><span class=\"c9 c1\">Students make their own flashcards to practice<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-1 start\">\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">FRONT: the number fact without the answer<\/span><\/li>\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">BACK: the answer along with a drawing to represent the strategy the student wants to use for that number fact.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ul class=\"c2 lst-kix_igm2y7pjfipi-0\">\n<li class=\"c5 c13 li-bullet-0\"><span class=\"c1 c9\">Occasionally students will do timed activities to measure progress towards automaticity<\/span><\/li>\n<\/ul>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c2 lst-kix_igm2y7pjfipi-1 start\">\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">This should NOT encourage students to race or &#8220;go as fast as they can&#8221;.<\/span><\/li>\n<li class=\"c8 c11 li-bullet-0\"><span class=\"c9 c1\">Students track their own progress on a chart.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p class=\"c5\"><span class=\"c1\">To my knowledge, there are not many fact fluency software programs that align with all the research for best practice. Existing software largely focus only on memorization and speed without building conceptual understanding. Two notable exceptions are\u00a0<\/span><span class=\"c14 c1 c15\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.mathfactlab.com\/&amp;sa=D&amp;source=editors&amp;ust=1762286597677403&amp;usg=AOvVaw09FYm2NiU880lf2n40hafr\">MathFactLab<\/a><\/span><span class=\"c1\">\u00a0and\u00a0<\/span><span class=\"c14 c1 c15\"><a class=\"c10\" href=\"https:\/\/www.google.com\/url?q=https:\/\/fluency.amplify.com\/&amp;sa=D&amp;source=editors&amp;ust=1762286597677678&amp;usg=AOvVaw2G_REbqX6FOMntOTRBwXnM\">Fluency By Heart<\/a><\/span><span class=\"c1 c15 c26\">.<\/span><\/p>\n<p class=\"c5\"><span class=\"c9 c1\">I hope this gets you started. Let me know if you need more information!<\/span><\/p>\n<p>.<\/p>\n<p>.<\/p>\n<p>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The other day I received a text from a school district I serve. It read, &#8220;On a scale of 1-10, how important is math fact fluency?&#8221; My answer: \u00a011 In a follow-up text, they asked for my thoughts on fluency instruction, fluency practice, and whether there are any online apps to support the development of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":3208,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[24,107,56],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/3206"}],"collection":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/comments?post=3206"}],"version-history":[{"count":2,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/3206\/revisions"}],"predecessor-version":[{"id":3209,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/3206\/revisions\/3209"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/3208"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=3206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=3206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=3206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}