{"id":1620,"date":"2021-04-15T17:59:06","date_gmt":"2021-04-15T22:59:06","guid":{"rendered":"http:\/\/blogs.mlc-wels.edu\/wels-educator\/?p=1620"},"modified":"2021-04-15T17:59:06","modified_gmt":"2021-04-15T22:59:06","slug":"moments-of-learning-in-mathematics","status":"publish","type":"post","link":"https:\/\/blogs.mlc-wels.edu\/wels-educator\/2021\/04\/15\/moments-of-learning-in-mathematics\/","title":{"rendered":"Moments of Learning in Mathematics"},"content":{"rendered":"

Written by Dr. James Carlovsky<\/em><\/p>\n

Important moments of learning do occur in a classroom. For many classroom teachers, these moments can be difficult to describe. \u201cSkilled teachers often recognize when important mathematical moments occur during a lesson\u201d (Leatham et al., 2015, p. 88). This article intends to shed light on these important moments of learning on behalf of the classroom students and their teachers.<\/p>\n

Pedagogical Moves<\/strong>
\n<\/em>So, what does a teacher do? These classroom student moments of learning often can lead to a classroom teacher action, also known as a pedagogical move (Jacobs et al., 2010). These moments of learning may lead a classroom teacher to ask a specific question, to revise a portion of a lesson, to refine what a classroom student has expressed, or even to test a classroom student in a formal or informal way (Lesh et al., 2003) So, what do teachers do in the process of student learning? Sherin suggested that \u201cemphasis on understanding the ideas that students offer is one of the hallmarks of mathematics education\u201d(2001, p. 84). A teacher should keep a focus on the student and their thought process.<\/p>\n

Learn from History!<\/strong>
\n<\/em>So, what do teachers usually do with their math lessons? A common perspective on learning in mathematics in the 20th<\/sup> century was that learning is the accumulation of knowledge, that practice solidifies mastery, and that knowledge is demonstrated by the ability to solve particular classes of problems (Schoenfeld, 2006).<\/p>\n

Get Students to Talk!<\/strong>
\n<\/em>Walshaw (2008) demonstrated that effective instructional practices demand students’ mathematical talk. Teaching focused solely on the acceptance of all answers and solutions does not strike at the core of what mathematics discourse truly entails. Mathematics teaching cannot be solely algorithmic or a fixation on the number of correct or incorrect answers that a student completes on a given assignment or assessment. Mathematics instruction and mathematics learning are so much more. When a teacher “presses a student to elaborate on an idea, attempts to encourage students to make their reasoning explicit, or follows up on a student’s answer or question with encouragement to think more deeply” (Morrone, et al., 2004, p. 29), the teacher is learning what students actually know and is providing an incentive for them to enrich that knowledge.<\/p>\n

Notice What Students Say!<\/strong>
\n<\/em>Davies and Walker (2005) focused on how teachers learned to notice significant instances of their students\u2019 knowledge probing. Knowledge probing could be described as grappling with content in a lesson. It is important to note that these teachers no longer focused their attention on lesson delivery, but rather on student interactions within a lesson. Other research is now beginning to probe how teachers question, revise and refine, test their content knowledge, and extend their knowledge to more powerful forms of classroom teaching (Lesh et al., 2003; Lesh & Doerr, 2003) for moments of learning on behalf of the students.<\/p>\n

Critical Moments<\/strong>
\n<\/em>An article by Thames and Ball (2013, p. 31) mentioned moments of learning as \u201ccritical hinge moments. In sizing up a student\u2019s answer, a teacher also has to coordinate hearing a student\u2019s thinking with a sense of whether or not the mathematical point is crucial at the moment.\u201d Some critical moments are opportunities to open up a topic to a student for learning as well as to help the students achieve the objective of a lesson.<\/p>\n

What\u2019s Your Goal?<\/strong>
\n<\/em>A classroom teacher can have a problem, can get all kinds of interesting things to come up, and can raise an interesting side trip during the lesson. However, more importantly, the teacher must keep an eye on the goals for the lesson and must coordinate decisions with whatever students are doing to get to that goal. This careful eye is the definition of skillful teaching, according to Ball (2005; 2010). Ball (1993) paid attention to the ideas of a student, not dismissing them as incorrect simply because they do not fit into the mathematical curriculum. The National Council of Teachers of Mathematics noted: “Effective teaching involves observing students [and] listening carefully to their ideas and explanations” (2000, p. 19).<\/p>\n

In Summary<\/strong>
\nResearchers have found that teachers\u2019 use of student thinking during mathematics instruction supports student learning of mathematics (Carpenter et al., 2006; Franke et al., 2007; National Council of Teachers of Mathematics, 2014; Van Zoest et al., 2016). Moments of learning do not have much value in the classroom for a teacher unless that classroom teacher notices that student learning or thinking and makes a pedagogical move. In summary, teachers should . . .<\/p>\n