Balanced Math Framework August 15, 2013
Getting to Know You... Math Style • Grab a bingo card from the middle of your table • Circulate the room searching for teachers who can "sign" a box on your bingo card (one signature per box please)
Math Workshop Readers and Math Writers = Workshop Workshop Framework Framework
Math Review is............. • Time to reinforce a previously taught concept • Formative and based on daily student understanding • Work that is de-briefed and discussed • Used to guide instruction • 3 to 6 review problems (based on grade level) • An opportunity to circulate and observe common misconceptions or understandings
Math Review is ............... • Not time to teach a new concept or trick the students • Not pre-printed or planned by yearlong or unit objectives • Not work completed without discussion • Not used as a grade or graded by others • Not more than six problems • Not busy work
Conceptual Understanding This is where you teach your curriculum. You will use Math Expressions, Glencoe and DMI experiences as a resource.
Standards for Mathematical Practice Mathematically Proficient Students... 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeating reasoning.
The Standards for Mathematical Practice Take a moment to examine the first three words of each of the 8 mathematical practices... what do you notice? Mathematically Proficient Students...
The Standards for [Student] Mathematical Practice What are the verbsthat illustrate the student actions of each mathematical practice?
Mathematical Practice #3: Construct viable arguments and critique the reasoning of others Mathematically proficient students: • understand andusestated assumptions, definitions, and previously established results in constructing arguments. • makeconjectures and build a logical progression of statements to explore the truth of their conjectures. • analyze situations by breaking them into cases, and can recognize and use counterexamples. • justify their conclusions, communicate them to others, and respond to the arguments of others. • reason inductively about data, making plausible arguments that take into account the context from which the data arose. • compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and-if there is a flaw in an argument-explain what it is. • construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. • determine domains to which an argument applies. • listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Standards for Mathematical Practice Buttons Task
Standards for [Student] Mathematical Practices • "Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking." ~ Stein, Smith, Henningsen, & Silver, 2000 • "The level and kind of thinking in which students engage determines what they will learn." ~ Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human 1997
Comparing Two Mathematical Tasks Martha was re-carpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase? ~ Stein, Smith, Henningsen, & Silver, 2000, p. 1
Comparing Two Mathematical Tasks Ms. Brown's class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits. 1. If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be? 2. How long would each of the sides of the pen be if they had only 16 feet of fencing? 3. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who read it will understand it. ~ Stein, Smith, Henningsen, & Silver, 2000, p.2
Comparing Two Mathematical Tasks Discuss: How are Martha's Carpeting Task and the Fencing Task the same and how are they different?
Comparing Two Mathematical Tasks Lower-Level Tasks Higher-Level Tasks
Reflection My definition of a good teacher has changed from "one who explains things so well that students understand" to "one who gets students to explain things so well that they can be understood." (Steven C. Reinhart, "Never say anything a kid can say!" Mathematics Teaching in the Middle School 5, 8 : 478)
Richard Schaar What I learned in school may be growing increasingly obsolete today, but how I learned to learnis what helps me keep up with the world around me. I have the study of mathematics to thank for that.
Rigor & Relevance Framework Relevance makes RIGOR possible, but only when trusting and respectful relationships among students, teachers, and staff are embedded in instruction. Relationships nurture both rigor and relevance.
Article: Tips for Using Rigor, Relevance and Relationships.
Rigor is... Work that requires students to work at high levels of Bloom's Taxonomy combined with application to the real world.
3 Misconceptions of Rigor •MORE – does not mean more rigorous. •DIFFICULT – increased difficulty does not mean increased rigor. •RIGID – “all assignments are due by… no exception.”
Relevance Why do I need to know this?
Misconceptions of Relevance •COOL – relevance doesn’t exclusively mean what the students do for “fun” •EXCLUSIVE – relevance without rigor does not ensure success.
Application Model 1.Knowledge in one discipline 2. Application within discipline 3. Application across disciplines 4. Application to real-world predictable situations 5. Application to real-world unpredictable situations