{"id":2847,"date":"2025-05-13T08:28:34","date_gmt":"2025-05-13T15:28:34","guid":{"rendered":"https:\/\/theothermath.com\/?p=2847"},"modified":"2025-05-13T08:28:34","modified_gmt":"2025-05-13T15:28:34","slug":"a-roadmap-for-improving-math-instruction","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2025\/05\/13\/a-roadmap-for-improving-math-instruction\/","title":{"rendered":"A roadmap for improving math instruction"},"content":{"rendered":"<p class=\"c6\"><span class=\"c1\">In this time of state testing, many educators are focusing on how to improve their math scores\u2026and rightly so. Rather than focusing on improving scores, let&#8217;s focus on improving mathematics instruction. The scores will take care of themselves.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">So\u2026how do we improve math instruction?<\/span><\/p>\n<p class=\"c6\"><img loading=\"lazy\" class=\"alignright\" title=\"\" src=\"https:\/\/lh7-rt.googleusercontent.com\/docsz\/AD_4nXc-LeXAvv_4ZH5C3KgluXHcxfcHJ2MjDvcFVHY_9RjvlGSjUL7BZin-jA9_iG8a2uP7RfJ1cO6FVTXKaTBxMDYai7NvSgffppopUTyIvXaEQVazR4aGKM0QDeNs0TEu17iPhCfZRw?key=OXpnipsG1QiiO9YQEZk80rJ4\" alt=\"\" width=\"256\" height=\"256\" \/><\/p>\n<p class=\"c6\"><span class=\"c1\">In this blog, I&#8217;ll share the six steps for improving math instruction in your school district or at your school site.<\/span><\/p>\n<ol class=\"c0 lst-kix_x32w7n4actde-0 start\" start=\"1\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">High expectations<\/span><\/li>\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Ambitious mathematics instruction<\/span><\/li>\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Sustained and on-going mathematics professional learning for teachers and administrators<\/span><\/li>\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Common assessments at the chapter level<\/span><\/li>\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Strategic intervention system<\/span><\/li>\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Establishing an accountability plan<\/span><\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<h1 id=\"h.yqxcnx88ptqo\" class=\"c2\"><span class=\"c9\">High expectations<\/span><\/h1>\n<p class=\"c3\">When teachers hold high expectations for their students, it significantly enhances student achievement and engagement.\u00a0<span class=\"c12\">The Opportunity Myth<\/span><span class=\"c1\">\u00a0(TNTP, 2018) highlights that many students are not given access to grade-level content, despite meeting classroom expectations, which limits their potential. When educators challenge students with rigorous material and believe in their ability to succeed, students demonstrate greater academic growth. Similarly, John Hattie&#8217;s meta-analyses (2009) show that teacher expectations have an effect size of 0.43, indicating a substantial impact on student learning. High expectations foster a culture of perseverance, self-efficacy, and deeper learning, ultimately preparing students for long-term success. When teachers&#8217; high expectations for their students is paired with the teacher&#8217;s own sense of self efficacy, the effect size jumps to an astounding 1.57!<\/span><\/p>\n<p class=\"c3\"><span class=\"c1\">Also in The Opportunity Myth, teachers with high expectations of their students are more likely to provide for their students access to grade-appropriate assignments, strong instruction, deep engagement, and high expectations. As a result, these students made significant academic gains, with those starting behind catching up at over five times the rate of their peers who did not receive such opportunities.<\/span><\/p>\n<p class=\"c3\"><span class=\"c1\">High expectations matter.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h1 id=\"h.fkzu2yl7hst2\" class=\"c2\"><span class=\"c9\">Ambitious instruction<\/span><\/h1>\n<p class=\"c3\"><span class=\"c1\">Defining what ambitious math instruction looks like in the classroom is essential to ensuring that all students engage in meaningful, rigorous mathematical learning. Cobb and Jackson (2011) emphasize that ambitious mathematics instruction goes beyond procedural fluency, focusing on deep conceptual understanding, reasoning, and problem-solving through student discourse and exploration.<\/span><\/p>\n<p class=\"c3\">The MCOE Math Team defines ambitious instruction through our\u00a0<span class=\"c4\"><a class=\"c11\" href=\"https:\/\/www.google.com\/url?q=http:\/\/mathhierarchy.com\/&amp;sa=D&amp;source=editors&amp;ust=1747153072653575&amp;usg=AOvVaw1jn0rAp7UjO9N9BS3Rkf6g\">Math Hierarchy of Needs framework<\/a><\/span><span class=\"c1\">.<\/span><\/p>\n<p class=\"c3\"><img loading=\"lazy\" class=\"aligncenter\" title=\"\" src=\"https:\/\/lh7-rt.googleusercontent.com\/docsz\/AD_4nXdLaSaEL3xL_npiF_olqskegE1_GyiQ3cNPaz8uWXyRPk3fQ4Xspi-IqDpXPWDzHQXL6Eb1uRnwf5GwnV_p11F-s0w27ewfi9Kl4H13RmISbzuLnvNOjmGix2L4tkYBQjwBTJQSLQ?key=OXpnipsG1QiiO9YQEZk80rJ4\" alt=\"\" width=\"366\" height=\"366\" \/><\/p>\n<p class=\"c6\"><span class=\"c1\">In the same way that Maslow\u2019s Hierarchy of Needs is a roadmap for how a person might experience the joy of experiencing self-actualization, with needs lower down in the hierarchy being satisfied before individuals can attend to needs higher up, the Math Hierarchy of Needs is a roadmap for how teachers and leaders might guide students towards becoming mathematically literate humans.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">Ambitious math instruction requires satisfying students&#8217; needs at each and every level. It is the role and responsibility of school districts to ensure that all five levels occur in each and every classroom.<\/span><\/p>\n<ol class=\"c0 lst-kix_575japldwakn-0 start\" start=\"1\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c10\"><strong>Material Needs:<\/strong> Teachers with math knowledge for teaching, essential standards, curriculum, math tools<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_575japldwakn-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Every student has a teacher with appropriate mathematics content knowledge and the pedagogical knowledge for teaching mathematics. \u00a0Math lessons are rooted in a solid understanding of the standards through rigorous, high-quality instructional materials employing mathematical tools that enhance student learning.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_575japldwakn-0\" start=\"2\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c10\"><strong>Mindset &amp; Culture:<\/strong> All students can learn, mistakes are normalized<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_575japldwakn-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Every student is immersed in a mindset and culture that intentionally communicates all students can learn math at high levels in an environment that considers each and every student\u2019s unique background, experiences, cultural perspectives, traditions, and knowledge. \u00a0Mistakes in mathematics are normalized. Students regularly experience high-quality, grade-appropriate lessons and assignments.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_575japldwakn-0\" start=\"3\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c10\"><strong>Student-centered Instruction:<\/strong> Meaningful discourse to promote conceptual understanding, procedural fluency, problem-solving, and application<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_575japldwakn-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Every student regularly experiences instruction that is student-centered and is designed to maximize students\u2019 use of language. Lessons create space for students to participate in discourse to promote conceptual understanding, which then leads to procedural fluency, problem-solving, and application.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_575japldwakn-0\" start=\"4\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c10\"><strong>Equitable Assessment:<\/strong> Feedback and intervention to achieve at grade level<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_575japldwakn-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Every student is regularly and humanely assessed in order to have understanding of their own growth and to receive productive feedback for next steps in learning. \u00a0Students use the feedback to know where they are in their learning, assess any misconceptions that need to be addressed, and then use the results to drive the next level of learning.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_575japldwakn-0\" start=\"5\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c10\"><strong>Math Literacy:<\/strong> Confident problem-posers and problem-solvers<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_575japldwakn-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Every student has the opportunity to analyze, reason, and communicate ideas effectively as they pose, formulate, solve, and interpret mathematical problems.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p class=\"c3\"><span class=\"c1\">While the math hierarchy might describe WHAT ambitious math instruction is, <a href=\"https:\/\/eric.ed.gov\/?id=EJ812134\" target=\"_blank\" rel=\"noopener\"><strong>Deborah Loewenberg Ball<\/strong><\/a> and her colleagues (2008) highlight the importance of a specific teacher skill called mathematical knowledge for teaching (MKT). She notes that effective math instruction only occurs when teachers skillfully facilitate discussions, pose high-quality questions, and respond to students\u2019 mathematical thinking in ways that advance understanding. Without a clear definition of ambitious instruction, classroom practices can vary widely, often reinforcing inequitable learning experiences. Establishing a shared vision ensures that teachers implement strategies that promote deep mathematical understanding and empower all students as capable problem-solvers.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h1 id=\"h.ydw0czuy15kr\" class=\"c2\"><span class=\"c9\">Sustained and Ongoing \u00a0PD and coaching<\/span><\/h1>\n<p class=\"c6\">It has long been recognized that\u00a0<span class=\"c4\"><a class=\"c11\" href=\"https:\/\/www.google.com\/url?q=https:\/\/theothermath.com\/index.php\/tag\/instructional-coaching\/&amp;sa=D&amp;source=editors&amp;ust=1747153072662395&amp;usg=AOvVaw0WPaQNu5QZZttiwCy-vWia\">mathematics-specific instructional coaching<\/a><\/span><span class=\"c1\">\u00a0leads directly to improved math instruction in the classroom and to increased student achievement. It is critical for teachers (in all stages of their career) to engage in curriculum-based professional learning in which they co-participate in teaching practices with instructional coaches through \u00a0the coaching cycle: lesson planning, observing instruction, debriefing the lesson.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">The professional development teachers receive should be short \u2013no more than three hours\u2013 and should focus on using the adopted curriculum teachers already have. Teachers learn how to effectively implement the curriculum in alignment with the recommendations of the California Mathematics Framework. The math coach leads the teachers through designing a lesson plan and then the team of teachers co-teach the lesson, which is then followed by a debrief session. Teachers reflect on the lesson and discuss changes they would want to make the next time they teach this lesson.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">The professional learning is then followed by in-class coaching to individual teachers. This provides teachers with the opportunity to implement the new teaching strategies with the math coach in the room to provide additional support as needed.<\/span><\/p>\n<p class=\"c6\"><img loading=\"lazy\" class=\"\" title=\"\" src=\"https:\/\/lh7-rt.googleusercontent.com\/docsz\/AD_4nXe2WGh45TaUHmYPs2qF-mlJUFUFeOsMPv69wOrvjq9Pk69nkPujaZ62jo1Jl1AIaBIY2nlx5ulQYj12IijzJGwUmNJKPXVSSi-Gsem64Zv3ZW8zumYBZ8Iu3JlKuw92hJ7cpCGddQ?key=OXpnipsG1QiiO9YQEZk80rJ4\" alt=\"\" width=\"701\" height=\"146\" \/><\/p>\n<p>&nbsp;<\/p>\n<h1 id=\"h.n83o1vbp6y5f\" class=\"c2\"><span class=\"c9\">Chapter-by-chapter common assessments<\/span><\/h1>\n<p class=\"c6\"><span class=\"c1\">Get rid of iReady. Get rid of NWEA.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">There\u2026I said it.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">Both of these products are seductive latchkey products that students can be plugged into and adaptively spit out some scores for each student. Ostensibly, these scores drive further instruction or intervention.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">The problem, however, these scores are meaningless for a variety of reasons.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">First, since the tests are adaptive, students are subjected to math content that is NOT grade-level appropriate. Both assessments treat math concepts as a sequence of stepping stones; each stone acting as a gateway before accessing the next stepping stone. The truth, however, is that mathematical concepts are more like an interconnected concept web providing a near infinite number of pathways from point A to point Z. For example, a latchkey testing product may prevent a 5th grade student from showing the grade-level content he has mastered simply because he does not know skills from previous grades such as how to read an analog clock or measure lengths with a ruler.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">The adaptive nature of both products also mean some students are exposed to problems from higher grade levels. Teachers then feel compelled to divert precious teaching time to content from other grade levels so that the data will show growth in the next testing cycle.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">A second issue with these products is they are comprehensive assessments that cover content that has not yet been taught. Students are frustrated by math concepts they have not yet been taught which could lead to math anxiety. Teachers are frustrated because they now have to scamble prior to each testing cycle to cram math content before the test that ordinarily would be taught later in the year. This wrecks havoc on the pacing and sequencing calendar teachers created during the summer.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">I could go on, but I&#8217;ll share just one last issue: The tests do not measure what, how, or whether the students are learning RIGHT NOW. If a teacher just taught fractions, the test should be on fractions. (Sure maybe some review questions thrown in.) The data of a fractions test immediately after teaching the fractions unit is useful for teachers and meaningful for students.<\/span><\/p>\n<p class=\"c6\">In California we have a FREE assessment system that ALL teachers can use instead of iReady and NWEA. The<span class=\"c14\"><a class=\"c11\" href=\"https:\/\/www.google.com\/url?q=https:\/\/www.caaspp-elpac.org\/&amp;sa=D&amp;source=editors&amp;ust=1747153072672800&amp;usg=AOvVaw0qTVc6vwCanLhmAlqBTbAx\">\u00a0CAASPP assessment system<\/a><\/span><span class=\"c1\">\u00a0provides a number of Interim Assessment Blocks (IABs) and Focused Interim Assessment Blocks (FIABs) that are grade-level appropriate and each covers a targeted math concept. The resulting data is useful because it is directly related to the content students just learned which allows the teacher to immediately plan meaningful intervention either embedded within future lessons or in a small-group setting.<\/span><\/p>\n<p class=\"c6\">Not in California? Or you teach a grade not tested by CAASPP? Then create grade-level common assessments that all teachers give. Get together to analyze the data to identify instructional strategies that work better than others. Use the data as the basis for teachers to form a learning community that encourages and engenders professional growth.<\/p>\n<p>&nbsp;<\/p>\n<h1 id=\"h.f4sqptxiylna\" class=\"c2\"><span class=\"c9\">Strategic Intervention system<\/span><\/h1>\n<p class=\"c6\">The data through the common assessments mentioned prior will undoubtedly identify students who need more support than can be embedded within future lessons. Students will need access to an effective strategic intervention system that aligns, supports, and integrates with the primary math instruction. Intervention should emphasize\u00a0<span class=\"c4\"><a class=\"c11\" href=\"https:\/\/www.google.com\/url?q=https:\/\/drive.google.com\/file\/d\/1j6Dkaq9k0gYXcN8Ytiftej6jC3M-jwug\/view?usp%3Dsharing&amp;sa=D&amp;source=editors&amp;ust=1747153072676274&amp;usg=AOvVaw0AMVcqDgkvmmC5EwUwAk2Y\">six recommendations<\/a><\/span><span class=\"c1\">:<\/span><\/p>\n<ol class=\"c0 lst-kix_q9i38w6b1se1-0 start\" start=\"1\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Recommendation 1: Systematic Instruction<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_q9i38w6b1se1-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Provide systematic instruction during intervention to develop student understanding of mathematical ideas.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_q9i38w6b1se1-0\" start=\"2\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Recommendation 2: Mathematical Language<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_q9i38w6b1se1-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Teach clear and concise mathematical language and support students\u2019 use of the language to help students effectively communicate their understanding of mathematical concepts.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_q9i38w6b1se1-0\" start=\"3\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Recommendation 3: Representations<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_q9i38w6b1se1-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Use a well-chosen set of concrete and semi-concrete representations to support students\u2019 learning of mathematical concepts and procedures.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_q9i38w6b1se1-0\" start=\"4\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Recommendation 4: Number Lines<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_q9i38w6b1se1-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_q9i38w6b1se1-0\" start=\"5\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Recommendation 5: Word Problems<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_q9i38w6b1se1-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Provide deliberate instruction on word problems to deepen students\u2019 mathematical understanding and support their capacity to apply mathematical ideas.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<ol class=\"c0 lst-kix_q9i38w6b1se1-0\" start=\"6\">\n<li class=\"c6 c7 li-bullet-0\"><span class=\"c1\">Recommendation 6: Timed Activities<\/span><\/li>\n<\/ol>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul class=\"c0 lst-kix_q9i38w6b1se1-1 start\">\n<li class=\"c6 c8 li-bullet-0\"><span class=\"c1\">Regularly include timed activities as one way to build students\u2019 fluency in mathematics.<\/span><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h1 id=\"h.lx0wdirz20na\" class=\"c2\"><span class=\"c9\">Accountability<\/span><\/h1>\n<p class=\"c6\"><span class=\"c1\">All partners need to perform their roles and responsibilities if we want to improve student mathematical achievement. District and site administrators who attend the math PD and demonstrations become equipped to support teachers through observing instruction in the classroom and identifying barriers to implementation of the targeted math initiative. Also, teachers would greatly benefit from a system of peer observations to learn from one another.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">Creating a strategy roadmap that clearly identifies the actions and goals of all the partners involved. Collecting data on the actions being implemented will enable barriers to be recognized and fixed as soon as possible.<\/span><\/p>\n<p class=\"c6\"><img loading=\"lazy\" class=\"\" title=\"\" src=\"https:\/\/lh7-rt.googleusercontent.com\/docsz\/AD_4nXcVExivRe_tzv42VMNLx8UoI8aoljU00_SWJ2GVZsNy1SSo8wjlxUOjP9Z8I_GeKvXojD98XbZwI6MXQpYZsM1e679CtP07Rw2UVeTtEbt6PSqx-DbMzLJ6bFR7jYm7M2DjzHNUOQ?key=OXpnipsG1QiiO9YQEZk80rJ4\" alt=\"\" width=\"663\" height=\"478\" \/><\/p>\n<p>&nbsp;<\/p>\n<h1 id=\"h.buemm0b0hugl\" class=\"c2\"><span class=\"c9\">In Conclusion<\/span><\/h1>\n<p class=\"c6\"><span class=\"c1\">The recipe for improving math instruction is not complicated. It is just six easy-to-understand things: high expectations, ambitious instruction, sustained support for teachers, frequent common assessments, strategic intervention system, and accountability.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">SIMPLE does not mean EASY, however. While the plan may be simple, carrying it out requires all partners to be patient, curious to learn new ways of teaching, and willing to navigate the uncertain and unfamiliar. For the sake of our students, let&#8217;s get to work.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">.<\/span><\/p>\n<p class=\"c6\"><span class=\"c1\">.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this time of state testing, many educators are focusing on how to improve their math scores\u2026and rightly so. Rather than focusing on improving scores, let&#8217;s focus on improving mathematics instruction. The scores will take care of themselves. So\u2026how do we improve math instruction? In this blog, I&#8217;ll share the six steps for improving math [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2848,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[92,126],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2847"}],"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=2847"}],"version-history":[{"count":3,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2847\/revisions"}],"predecessor-version":[{"id":2851,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/2847\/revisions\/2851"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/2848"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=2847"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=2847"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=2847"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}