{"id":463,"date":"2019-03-22T07:17:47","date_gmt":"2019-03-22T14:17:47","guid":{"rendered":"http:\/\/theothermath.com\/?p=463"},"modified":"2025-05-06T12:12:14","modified_gmt":"2025-05-06T19:12:14","slug":"the-effect-of-great-math-teaching","status":"publish","type":"post","link":"https:\/\/theothermath.com\/index.php\/2019\/03\/22\/the-effect-of-great-math-teaching\/","title":{"rendered":"The effect of great math teaching"},"content":{"rendered":"

Updated 5\/6\/2025: Added information about recent NCTQ report.<\/strong><\/em><\/p>\n

 <\/p>\n

Teachers matter. Good teaching matters. In this week of Teacher Appreciation, I am reminded of an experience many years ago…<\/p>\n

After school one day, I wandered into the classroom of a new teacher to check how her day went. I saw this on her chalkboard\u2026<\/p>\n

\"five<\/p>\n

After a brief chat about the answer, it was clear that she indeed thought that any number raised to the zero power was equal to zero. Doing my best of embody the famous quotation of G.H. Hardy, \u201cA mathematician, like a painter or a poet, is a maker of patterns\u201d<\/em>, I created a table of some powers of 5. Then we gradually completed the table together.<\/p>\n

\"table<\/p>\n

Finally, we looked for patterns in the table. Looking at the middle column, my colleague said, \u201cSee? The fives are gradually disappearing. There will be no fives for 5 to the power of 0, so the answer is zero.\u201d<\/p>\n

\u201cThat seems to make sense, but let\u2019s look at the third column. What is happening as we move down the column?\u201d, I asked.<\/p>\n

\u201cIt divides by 5\u201d, replied. I filled in the table only to hear her gasp in amazement. \u201cOh my gosh! It\u2019s ONE!\u201d, she almost screamed.<\/p>\n

\"table<\/p>\n

\u201cBut what about the middle column?\u201d, she wondered out loud to herself.<\/p>\n

\u201cYou were half right\u201d, I said. \u201cThere are no fives…but the answer is one, not zero.\u201d<\/p>\n

\u201cBecause the pattern says so?\u201d she asked. And before I could say anything, she confirmed her own answer by repeating herself, \u201cBecause the pattern says so!\u201d<\/p>\n

Good teaching matters<\/h3>\n

Long ago I stumble upon this wonderful article<\/strong><\/a> on the impact of teacher effectiveness on student achievement. If my colleague was unintentionally teaching her students misinformation with exponents, where else might she have been misinforming or half-informing her students. What impact might this have on her students?<\/p>\n

Now…I\u2019m NOT bagging on my colleague. It is not her fault that no one taught her this simple \u201cproof\u201d of the Zero Exponent Rule. I\u2019m honored to have taught her a little something. Indeed, she grew to become a great teacher, only the tiniest part because of me. For that moment, however, I performed the role of mathematics instructional coach, helping her with both mathematics AND the instructional strategies that might be used to get the mathematics across to the students. As a result, she took a huge step towards being a high performing teacher.<\/p>\n

Why does this matter? In this research progress report<\/strong><\/a>, we learn that there is a huge difference in student academic achievement depending on whether the students experience three consecutive years of high-performing teachers versus three consecutive years of average-performing or low-performing teachers.<\/p>\n

\"high<\/p>\n

In comparing 5th grade math achievement after experiencing three consecutive years with high-performing teachers versus three consecutive years with low-performing teachers, the report states, \u00a0\u201cWith an even start, the difference in these two extreme sequences resulted in a range of mean student percentiles in grade five of 52 to 54 points!!\u201d<\/p>\n

In a nutshell…GOOD TEACHING MATTERS!<\/strong><\/p>\n

Unfortunately, the effect of student achievement after experiencing a low-performing teacher for a single year can still be measured even after multiple years of having high-performing teachers. It is essential that we properly support teachers in growing their math knowledge and pedagogical knowledge, such that no student is subjected to the instructional strategies of low-performing teachers. Or at least, site administrators can insure that students who experience a year with a low-performing teacher should then experience multiple years of high-performing teachers. A recent report<\/strong><\/a> (April, 2025) from the National Council on Teacher Quality found virtually no graduate elementary prep programs dedicate sufficient time to preparing teachers on how to teach math and on the essential math content they should know. Undergraduate programs are doing better on average, but many still fail to meet the minimum expectations for math content instruction.\u00a0 Moreover, many teachers say math makes them anxious<\/strong><\/a>, which has proven to negatively impact student learning.<\/p>\n

GOOD TEACHING MATTERS!<\/strong><\/p>\n

Since it is so obvious that the quality of the math instruction is of paramount importance, we teacher leaders and math leaders need to be vociferous advocates for meaningful mathematics coaching. Occasional sit-and-get professional development is not good enough. We need the kind of ongoing training and coaching that will bring about real change in the classroom.<\/p>\n

Our teachers and our students deserve it.<\/p>\n

.<\/p>\n

.<\/p>\n

.<\/p>\n","protected":false},"excerpt":{"rendered":"

Updated 5\/6\/2025: Added information about recent NCTQ report.   Teachers matter. Good teaching matters. In this week of Teacher Appreciation, I am reminded of an experience many years ago… After school one day, I wandered into the classroom of a new teacher to check how her day went. I saw this on her chalkboard\u2026 After […]<\/p>\n","protected":false},"author":1,"featured_media":469,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[103,19,51,46],"_links":{"self":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/463"}],"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=463"}],"version-history":[{"count":8,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/463\/revisions"}],"predecessor-version":[{"id":2846,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/posts\/463\/revisions\/2846"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media\/469"}],"wp:attachment":[{"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/media?parent=463"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/categories?post=463"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theothermath.com\/index.php\/wp-json\/wp\/v2\/tags?post=463"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}