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This article will be my attempt to convince you why.  \nFor 13 years, I have taught math (or “maths,” as I like to call it) to students ages 11 to 18 in the United Kingdom. For much of my career, I did not reflect on why I was doing the things I did. I was  \nCraig Barton has taught math to secondary school students in the United Kingdom for 13 years. He is the creator of the websites [www.mrbarton](www.mrbarton)[ ](www.mrbarton)[maths.com](maths.com), which offers free math support and resources to teachers and students, [and www.diagnosticquestions.com](and www.diagnosticquestions.com), which contains the world’s largest collection of free diagnostic multiple-choice math questions. He is also the host of Mr Barton Maths Podcast, which features interviews with inspiringfigures in education. This article is adapted with permission from his book, How IWish I’d Taught Maths: Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes (John CattEducational, 2018).  \nresults and seemed to enjoy their lessons, and that was good enough for me. It was only when I started my Mr Barton Maths Podcast that my cozy little world began to crumble.* Interviewing educators from around the world really made me stop and question practices that I had done for many years without really thinking about them. These conversations led to two years of reading hundreds of books and research articles; trying, failing, and tweaking new ideas with my students; and eventually writing a book: How I Wish I’d Taught Maths: Lessons Learned from Research, Conversations with Experts, and 12 Years of Mistakes.  \nOne of those key mistakes I made was to ignore the immense power of formative assessment.  \nFormative assessment is a phrase that is bandied around a lot. It is something all teachers are told we have to do, but often without any real substance or conviction. It is marketed as a generic teach-  \n*Mr Barton Maths Podcast features interviews with leading figures in education. To access all the episodes, [visit www.mrbartonmaths.com/podcast](visit www.mrbartonmaths.com/podcast).  \nILLUSTRAT IONS BY KASIA BOGDANSKA  \nAMERICAN EDUCATOR | SUMMER 2018 33  \ning strategy—one that can be used across all subjects—and so it is usually accompanied by whole-school training sessions, where us mathematics teachers are presented with examples from English, history, and geography and persuaded that they will definitely work forthelikes of equations, percentages, and histograms.  \nSo for much of my career, I steered clear of any mention of formative assessment. Then I came across the work of Dylan Wiliam, an expert on the topic. And it is a good thing I did, because Iam now convinced that teaching without formative assessment is like painting with your eyes closed.  \nIn 2016, Wiliam sent the following tweet: “Example of really big mistake: calling formative assessment ‘formative assessment’rather than something like ‘responsive teaching.’”  \nIndeed,“responsive teaching” feels like a much better description to attach to the tools and strategies I will discuss here. The word “assessment” conjures up visions oftests and grades. For teachers, it means more work, and for students, more pressure. While it’s important to see tests as tools of learning, the association with assessment has probably not helped the development and adoption of this most valuable of strategies.  \nPaul Black, a prominent researcher on formative assessment, and Wiliam explain that an assessment functions formatively “to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers, to make decisions about the next steps in instr","cbCaic84Jwk8QWlz","https://ap.wps.com/l/cbCaic84Jwk8QWlz","pdf",440264,"English","# On Formative Assessment in Math\n## How Diagnostic Questions Can Help","[{\"question\":\"What does the article claim is the single most important teacher practice each lesson?\",\"answer\":\"Asking and responding to diagnostic questions is presented as the single most important thing done in every lesson.\"},{\"question\":\"How does the article define formative assessment in practice?\",\"answer\":\"Formative assessment functions when evidence about student achievement is elicited and interpreted to make next instructional decisions that are better than without that evidence.\"},{\"question\":\"Why does classroom culture matter for diagnostic questioning?\",\"answer\":\"If students fear making mistakes, they may stay silent; the article argues students need a culture where questions and responses are safe so teachers can access useful information about understanding.\"}]","On Formative Assessment in Math - How Diagnostic Questions Can Help | PDF",1792072797,18]