"The Math Ceiling" - from Math with Bad Drawings blog
Do we have a "math ceiling" where some math is beyond our ability to comprehend? If a student can perform the math task I am targeting without conceptual understanding (i.e., they know the procedure, but not why it works), do they really need more?
TAGS: conceptual understanding, fixed, growth, mindset, procedure, algorithm
Achieve the Core
The site describes itself as "full of free content designed to help educators understand and implement the Common Core and other college and career ready standards." Resources include CCRS-aligned tasks, but also materials to support educators in understanding the standards and the content.
TAGS: Common Core, CCRS
Concept, Method, Procedure (The Secret Formula for Math Success)
Max Ray, of The Math Forum, explores developing procedures from conceptual understanding. His 5-minute video uses dividing by fractions as the topic for instruction.
TAGS: conceptual understanding, procedure, 5.NF.5, 4.NF.4b, 4.NF.4a, 4.NF.4b, 4.NF.4c, 5.NF.6, 5.NF.7, 5.NF.7b
Fluency Without Fear
Turns out memorization, timed tests and flash cards are not the most effective ways to learn math facts. What?! What are the alteratives? This arcticle addresses developing students' fluency with math facts (such as times tables), including confidence and how some common approaches to math facts can be related to anxiety and loss of perseverance. The difference between number sense – where students can flexibly use their understanding – and memorization is addressed. Speed and mathematical ability are also addressed. The author describes what research suggests for best practices in building fluency. In the second half of the article, the author suggests various strategies teachers can use to build their students' number sense and fluency.
TAGS: Procedural Skill and Fluency, math facts, number sense, Jo Boaler, conceptual understanding, number talks, math facts, times tables
Mistakes vs. Errors
Encouraging mistakes and exploration of mistakes is part of a growth mindset. Aiming for accurate answers is also important. This teacher writes about bringing both of these into the classroom.
TAGS: growth mindset, SERP, Cole
Free problems ranging from counting to high school equivalent (HSE) content. You can search by Common Core Standard, content topic, or grade level.
The page offers a problem solving worksheet that aligns well to the CCRS Mathematical Practices. (The sheet may need to be revised for some English learners or students with low literacy.)
TAGS: CCRS, open-ended, multiple solutions, mtbos, #mtbos, Kaplinsky
Why Before How
Why Before How: Singapore Math Computation Strategies. Hazekamp, Jana (2011). Available at many libraries, bookstores, through Amazon and Powell's, etc. (ISBN-13: 978-1934026823)
Hazekamp explores strategies for building number sense around place value and basic operations.
From the publisher:
Jana Hazekamp introduces a wide variety of computation strategies, adapted from the acclaimed Singapore approach, that will bring students a real understanding of number relationships and the meaning behind the math. The guided-conversation format is designed for quick reading, and Jana's question-and-answer style is particularly well suited to encouraging students to focus on the why and to begin using math terminology correctly and fluently.
Teachers can use this book to build the concept of place value, encourage students to consider multiple methods for solving problems, and build real understanding of the meaning behind addition, subtraction, multiplication, and division paving the way to beginning algebra.
These strategies can be used for whole-class instruction and also for small intervention groups. The book does not have to be read cover to cover; the reader can dip in as needed to help a student who's struggling with a particular concept. (See more at Powell's)
TAGS: book, number sense, operations, CCRS, Level A, Level B, Level C, conceptual understanding