Part 1: Math Methodology: Instruction

Our first version of this first essay's beginning is casual, to say the least. Some of the language, the choice of words, would be typical of friends standing in front of a painting at the museum, remarking in an off-handed way some of its more obvious characteristics. Words and phrases such as "guy," "pretty much," "horse's rear end," "weird thing," "give a darn," "pretty," and, of course, "Whoa, Nelly!" would be inappropriate in formal academic discourse. It's not so much that those words are , exactly, just that they are neither precise nor helpful in our understanding of how the painting registers its effects on the viewer. In addition, the analysis of the painting is done entirely from the viewpoint of the first-person singular, "I." Again, that's not exactly wrong, but the reader is impressed by the fact that these impressions could be entirely those of the eccentric individual writing, not that these are impressions that ought to be shared by others.

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Assessment includes both traditional paper-and-pencil exams, such as those made up of True/False, short-answer, or multiple-choice items, and a much larger collection of procedures that teachers can use to get a fix on their students' status, including the use of portfolios to document students' evolving skills and the use of anonymous self-report inventories to measure students' attitudes or interests. Assessments also include the variety of informal techniques a teacher might use to check on the status of students' skills for the purpose of guiding instruction rather than for grade-giving, such as when a teacher periodically projects multiple-choice questions on a screen during a lesson and asks students, "on the count of three," to hold up one of four prepared index cards showing the letter of what each student believes is the correct answer. (Popham, 2009, Preface section, para. 6)

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The Instruction Essay (Page 1 of 3) on this page contains the following subsections:

As an alternative to determining learning styles, a personal and based on Gardner's work will also benefit teaching and learning. Students with learning disabilities or attention-deficit-disorder can find practical tips on how to make your learning style work for you at , which also contains more information on multiple intelligences.

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W. James Popham (2009) summed up the nature of teaching in the 21st century. He stated, "once we strip away its external complexities, teaching boils down to teachers' deciding what they want their students to learn, planning how to promote that learning, implementing those plans, and then determining if the plans worked" (Preface section, para. 7). So where does one begin?

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Resources on the current page will assist you with your knowledge of students and instructional practices. CT4ME's section on includes a variety of resources to assist you with becoming more knowledgeable about the mathematics content you teach and how to enhance your teaching skills. Our section on provides solid advice and resources. will assist you with strategies for incorporating technology into your instruction, including designing your classroom web site, and incorporating multimedia into math projects. You can learn more about scientifically based research and action research at our section.

Learn more about math pedagogy from math educators around the world.

Teaching experience matters (Kini & Podolsky, 2016). "What distinguishes the beginning from the accomplished teacher is the degree of sophistication in the application of the knowledge and skills" (Council of Chief State School Officers, 2011, p. 8). However, years of experience does not equate to being an expert. From a review of literature and a synthesis of over 500,000 studies on differences between experience and expertise in teaching, Hattie and colleagues (2003) identified five major dimensions illustrating the expertise of excellent teachers and then elaborated on 16 attributes within those. Expert teachers: