1. Printing: Your printer might not print the same way our printers do, so make sure to try a couple of test prints. If things aren’t aligning quite right, experiment with the Scale to Fit Paper setting. It’s located in the Print dialog – just click Full Page Slides to get to it. And did you notice we made fold marks for you? They are really light, but if you don’t like them showing on your brochure, click View, Slide Master, and delete them before you print. Customizing the Content: The placeholders in this brochure are formatted for you. If you want to add or remove bullet points from text, just click the Bullets button on the Home tab. If you need more placeholders for titles, subtitles or body text, just make a copy of what you need and drag it into place. PowerPoint’s Smart Guides will help you align it with everything else. Want to use your own pictures instead of ours? No problem! Just click a picture, press the Delete key, then click the icon to add your picture. If you replace a photo with your own and it’s not a flawless fit for the space, you can crop it to fit in almost no time. Just select the picture and then, on the Picture tools Format tab, in the Size group, click Crop. Mathematics Teaching and Learning Philosophy References Hiebert, J., Carpenter, T.P., Fennema, E., Funson, K.C., Wearne, D., Murray, H. Olivier, A., & Human, P. (1997). Introducing the critical features of classrooms. Making sense: teaching and learning mathematics with understanding (pp. 1-15). Portsmouth, NH: Heinemann. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). The strands of mathematical proficiency. Adding it up: helping children learn mathematics (pp. 115-155). National Academic Press. Kersaint, G. The learning environment: its influence on what is learned (pp. 83-96). Suh, J. M. (2007). Tying it all together: classroom practices that promote mathematical proficiency for all students (pp. 163-169). The National Council of Teachers of Mathematics, Inc. Barlow, A. T., & Cates, J. M. (2007). The answer is 20 cookies; what is the question? (pp. 252-255). The National Council of Teachers of Mathematics, Inc. Malloy, C. E. (Ed.). (2009). Mathematics for every student: responding to diversity. Virginia: National Council of Teachers of Mathematics. Smith, M. S., & Stein, M. K. (2011). 5 Practices for orchestrating productive mathematics discussions. Virginia: National Council of Teachers of Mathematics. “Equity, in part, means that each student is treated as an individual, and listening, really listening, is one of the best ways to encourage such treatment.” ~ Authors of Introducing the Critical Features of Classrooms By: Marin Beck How will I provide equitable opportunities for all students to learn mathematics? Every student has the right to understanding in mathematics, and equity in the classroom ensures that this happens. The fundamental principle of equity is treating each child as the individual that he or she is, and providing what is needed for that child to be successful. This can only be done if the teacher knows the students— their cultures, experiences, prior knowledge, strategies, and preferences. This is accomplished when the teacher goes beyond hearing his or her students, and graduates to listening to them. When a child is both known and respected, a beautiful thing happens. The authors of Introducing the critical features of the classroom say that “Both of these remove stereotypes and eliminate expectations that might be tied to particular group memberships.” When such biases are removed, teachers can be free to provide equitable opportunities to all students.

2. Printing: Your printer might not print the same way our printers do, so make sure to try a couple of test prints. If things aren’t aligning quite right, experiment with the Scale to Fit Paper setting. It’s located in the Print dialog – just click Full Page Slides to get to it. And did you notice we made fold marks for you? They are really light, but if you don’t like them showing on your brochure, click View, Slide Master, and delete them before you print. Customizing the Content: The placeholders in this brochure are formatted for you. If you want to add or remove bullet points from text, just click the Bullets button on the Home tab. If you need more placeholders for titles, subtitles or body text, just make a copy of what you need and drag it into place. PowerPoint’s Smart Guides will help you align it with everything else. Want to use your own pictures instead of ours? No problem! Just click a picture, press the Delete key, then click the icon to add your picture. If you replace a photo with your own and it’s not a flawless fit for the space, you can crop it to fit in almost no time. Just select the picture and then, on the Picture tools Format tab, in the Size group, click Crop. How do children learn mathematics? Building this disposition is essential to success in mathematics. There are several ways to promote positive dispositions in students, including: Providing authentic problems that need to be solved Modeling math problems in your life, and asking students to find math problems in their everyday lives as well Allowing students autonomy to use the method of their choice in solving problems Providing problems at the appropriate level, and leaving them open ended to allow for the success of all students via differentiation according to ability level In order for a child to truly learn mathematics in a meaningful and lasting way, instruction must build five separate, but related, understandings. These are the five strands of mathematical proficiency, which include conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Instruction can certainly build each of these strands (and mathematical proficiency as a whole); however, students must develop their own schema, or way of thinking about mathematics. The teacher’s role is thus to: Provide rich activities that place mathematics within an authentic context Generate discovery Allow students to complete problems in a variety of ways with various materials Support the transfer of mathematical principles to new situations Encourage students to communicate with one another to test their ideas and hear other perspectives Support the practice of metacognition to understand the concepts behind the procedures Help students self-reflect in order to identify their own misconceptions. When all of these practices are upheld, children’s learning of mathematics will be boundless. The instructional strategies employed by any educator are numerous. Though this list is not exhaustive, it indicates those I find to be most important or employ most frequently. Fostering a positive learning environment by holding high expectations and providing equitable opportunities to learn Communicating learning targets to students so that they can feel responsible for their own learning Employing mathematically rich tasks, such as asking, “What is the question?” Using discussion and social interaction to build mathematical literacy, while maintaining student’s accountability Using diverse learners as resources for enriching math education How would I promote positive dispositions towards mathematics learning? A productive disposition toward mathematics is, “The habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy,” according to Jennifer Suh, author of Tying it all Together. What instructional strategies might I use? Should students be assessed? How? Student assessment is always an important part of teaching, but there is a time and place for it, and it need not always be formal. Monitoring during math instruction is one informal way of assessing students. It allows the teacher to discover which strategies a student is using, as well as identify misconceptions and misunderstandings the student might have. This data should then be used to inform instruction, whether students who are struggling need more guidance and support, or students who have achieved mastery need opportunities to extend and deepen their thinking.