3 33 What difference did a few seconds make for you cognitively? Emotionally? What difference did a few seconds make for you cognitively? Emotionally? What impact do you think this has on our students? What impact do you think this has on our students? Reflection
Close Read Fluency: Simply Fast and Accurate? I think Not! 1.Number Paragraphs 2.Underline important details 3.Circle things you disagree with /confused about 4.Write Ahas! In the margins http://www.nctm.org/about/content.aspx?id=34791
The main consideration is that timed situations creates stress for the students, which lowers the efficiency of the brain, especially in the situation of new learning. Susan Mastering the Basic Math Facts in Addition and Subtraction Susan O’Connell and John SanGiovanni
The animation is already done for you; just copy and paste the slide into your existing presentation. The Common Core State Standards for Mathematics (CCSSM) document describes procedural fluency as “skill in carrying out procedures flexibly, accurately, efficiently, and appropriately ”. (CCSSI 2010, p. 6)
The animation is already done for you; just copy and paste the slide into your existing presentation. Fluency includes three ideas: Efficiency Efficiency –carrying out the strategy easily. Accuracy Accuracy - depends on precise recording, knowledge of number relationships, and checking results. Flexibility Flexibility -requires the knowledge of more than one approach to solve the problem and to check the results. “ Developing Computational Fluency with Whole Numbers in the Elementary Grades” – Susan Jo Russell
Mathematics Fluency: A Balanced Approach http://www.youtube.com/watch?v=ZFUAV00bTwA
Developing fluency requires a balance and connection between conceptual understanding and computation proficiency. Computational methods that are over-practiced without understanding are forgotten or remembered incorrectly. Understanding without fluency can inhibit the problem solving process. NCTM, Principles and Standards for School Mathematics, pg. 35
Conceptual Understanding Develop strong understanding of operations and number relationships through problem posing, hands-on exploration, real-world examples, classroom discussion, exploring situations through literature Susan O’Connell and John SanGiovanni, Mastering the Basic Math Facts (Heinemann 2011) John A. Van De Walle, Teaching Developmentally (Pearson, 2004). Strategic Thinking Develop efficient strategies for fact retrieval. Help students see the possibilities and then let them choose strategies that help them determine the answer without counting.
Practice for Fluency Provide drill with efficient strategies Scatter practice 5-10 min. day Use a variety of practice activities to keep students motivated Use groups of related facts Avoid too many facts too quickly Practice basic facts in Math Review and Mental Math Susan O’Connell and John SanGiovanni, Mastering the Basic Math Facts (Heinemann 2011) John A. Van De Walle, Teaching Developmentally (Pearson, 2004).
Drill can strengthen strategies with which students feel comfortable—ones they “own”—and will help to make these strategies increasingly automatic. Premature “Premature drill introduces no new information and encourages no new connections. It is both a waste of time and a frustration to the child.” Van de Walle & Lovin, Teaching Student-Centered Mathematics Grades K-3, pg. 117
Differentiation Strategies For older students needing remediation: Traditional Drill will not work Pre-assess known and unknown facts Diagnose strengths and weaknesses Provide hope! Build success! Source: John A. Van De Walle, Teaching Developmentally (Pearson, 2004).
The animation is already done for you; just copy and paste the slide into your existing presentation.
Assessing Students Assess progress informally/formally Develop procedures for keeping track of student data Consider using time as a personal motivator – “beat their own record” Have students track their own progress The goal of fact checks/test should be to identify additional instructional needs.
One more/two more Facts with zero Doubles Near-doubles (6 + 7 = 6 + 6 + 1 = 13) Ten frame/five frame Subtraction— think addition, build up through 10 (13 – 9, 15 – 8) Addition and Subtraction Key Patterns:
Multiplication and Division Patterns: Doubles Fives Zeros and ones Nines Helping facts (3 x 8 connected to 2 x 8 — doubles plus 8 more) Multiplication before division Division’s connection to multiplication
The animation is already done for you; just copy and paste the slide into your existing presentation. Children must master the basic facts because those who continue to struggle with basic facts often fail to understand high mathematics concepts. Their cognitive energy is spent doing computation when it should be spent focusing on the more sophisticated concepts being developed. (Forbringer & Fahsl, 2010)
Group Discussion How do you currently teach and assess math facts at your grade level? What are the most significant ways in which we should rethink teaching of math facts?