{"id":3525,"date":"2021-09-02T05:01:39","date_gmt":"2021-09-02T09:01:39","guid":{"rendered":"https:\/\/isa.swintonstudio.com\/Home\/?p=3525"},"modified":"2021-09-03T02:54:55","modified_gmt":"2021-09-03T06:54:55","slug":"the-wonder-of-questions","status":"publish","type":"post","link":"https:\/\/isa.swintonstudio.com\/Home\/the-wonder-of-questions\/","title":{"rendered":"The Wonder of Questions"},"content":{"rendered":"\n

Questions, to me, are wonder-filled. An invitation to explore. They are both the beginning of a quest to understand and the fuel for the quest\u2019s continuation. This is, in part, why questions are an essential part of our work with teachers, school, and district leaders as we collaborate to cultivate inquiry-focused instruction<\/a> in classrooms and support school communities in their continuous improvement efforts. As we close out an unprecedented school year, many questions are being asked about the instructional ramifications of this year for the start of next school year, when many more schools expect live in-person instruction to be more prevalent. Conversations are happening across the spectrum, from discipline-focused professional organizations to grade-level teams in schools.<\/p>\n\n\n\n

As a former mathematics teacher, I\u2019m particularly attuned to the conversation as it relates to mathematics.<\/p>\n\n\n\n

Recently, the National Council of Teachers of Mathematics (NCTM) held a webinar to focus was on how to support students next year. Webinar panelists made a number of wonderful points about meeting the whole student where they are next year. Among the exhortations from the panelists was a call to maintain focus on grade-level standards and to hone in on the big ideas, those that span grade levels and standard bands. In other words, what are the big questions that help us get deeper as the content evolves? I love these kinds of questions because they can accentuate the coherence inherent in mathematics. So I wanted to offer one question I\u2019ve used with students and teachers that has helped deepen connections and focus on one of the big ideas within mathematics: What is the power of equality?<\/p>\n\n\n\n

This question asks that we understand (a) the relational essence of equality, (b) the way equality manifests in different mathematical representations, and (c) the way in which maintaining the relationship allows us to manipulate expressions and solve problems. As a question that can span grade levels and standard bands, \u201cWhat is the power of equality?\u201d works for elementary students beginning to understand the relational essence when using operations (1 + 2 = 3) or placing equivalent numbers or expressions at the same place on a number line, so that we see that equality doesn\u2019t require that equivalent numbers or expressions look the same (3\/4 = 6\/8 = 0.75 = 1 \u2013 1\/4 = 1\/2 + 1\/4). This question also works for middle school students, as they begin to solve equations by keeping the expressions on each side equivalent or comparing the rates of change of linear relationships. The algebra student solves systems of equations and substitutes an expression for a variable because they are equivalent. The examples could continue into other parts of mathematics. Thus, \u201cWhat is the power of equality?\u201d is a question that can travel with students.<\/p>\n\n\n\n

Often, we wonder how to connect mathematical content to historical, political, and social moments. Considering this with equality in mind, there\u2019s an opportunity to engage our students in dialogue about,<\/p>\n\n\n\n