Archive for April, 2011
Math Millionaire Games! Great Fun and Learning
See this link for some great upper elementary and middle school math games!
The algebraic expression millionaire game is great! So is the division one!
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( 1 so far )More about Fractions: Do the Work in Guided Math Groups
The National Math Report said a great deal about fractions in elementary school. Here are a few of the research highlights (p 17-18):
- Pictorial representations, without sufficient emphasis on the nature of wholes …may be an obstacle
- Number line representation may be more effective.
- Words also seem to influence the mental representations that children form concerning fractions
Recommendations
- Focus on conceptual knowledge first
- Procedural knowledge is equally important
Successful Interventions include:
- the use of fraction names that demarcate parts and wholes,
- the use of pictorial representations that are mapped onto the number line,
- composite representations of fractions that are linked to representations of the number line.
- Conceptual and procedural knowledge about fractions less than one do not necessarily transfer to fractions greater than one, and must be taught separately.
Curriculum:
Spend time doing fractions and proportional reasoning… with the goal for students being one of learning rather than performance. However, there should be ample opportunity in the curriculum for accurate self-evaluation.
What do you think of that? Number lines are big here! Pull out the number lines when you teach fractions…Also, self-evaluation keeps coming up. Do you give your students time to self-evaluate? How does that look across the grade levels? Notice the emphasis on a learning rather than just performing. We want students doing WITH understanding!
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( 1 so far )Fractions: Work it out in Guided Math Groups
Fractions
The National Math Report has a great deal to say about Fractions. First it notes that although fractions, decimals and proportions are introduced early on, many folks (adults included) still have problems problem solving with them! There should be an emphasis on “understanding and manipulating fractions.” This type of work is done in small guided math groups so you can build understanding at the concrete, pictorial and abstract level and you can work with a variety of manipulatives.
“A fraction is defined as a point on the number line, based on the concept of a part whole relation, with the unit segment [0,1] (the segment from 0 to 1) serving as a whole.”
The Report notes that to fully assess students understanding we have to distinguish between the difference of students “formal fractional notation” and “their intuitive ability to understand fractional relations and perform calculations using fractional quantities.”
Many of the mistakes regarding fractions are due to “faulty procedure. Children’s accuracy at recognizing formal procedural rules for fractions and automatic retrieval of basic arithmetic facts predicts computational skills, above and beyond the influence of intelligence, reading skills, and conceptual knowledge.”
The research shows that the more they work with fractions the more their conceptual knowledge grows. Most interestingly “motivation also has positive effects on fraction learning. Learning goals rather than performance goals may produce higher self-efficacy, skill, and other achievement outcomes in students. Performance goals with self-evaluation components may be more effective than without.”
How do you teach fractions now? How much time do you spend on building conceptual understanding? In the New Common Core, starting at 3rd grade, fractions has its own domain. I encourage everyone to talk on the grade level about the differences between learning goals and performance goals. Note what the report states. Do you have a self-evaluation piece for students as part of your performance goals?
See this great resource from the Center for Comprehensive Reform and Improvement : Beyond Slices of Pizza: Teaching Fractions Effectively
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( None so far )If they think they can…they can: Building Belief in Guided Math Groups
The National Math Report states that:
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children’s belief’s about the relative importance of effort and ability can be changed;
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increased emphasis on the importance of effort is related to greater engagement and persistence on mathematics tasks;
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improved mathematics grades result from these changed beliefs.
If we teach them they can, they can.
If we give them guided practice and instant feedback, they can.
If they practice with purpose in centers, they can.
If we believe they can, they can.
If they believe they can, they will.
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( 1 so far )Math Anxiety: Addressing it in Whole Group and Small Group Discussions
We are in the middle of testing season. Children’s emotional state of being can definitely impact how they do on their math exams. The National Math Report states that “Anxiety is an emotional reaction that is related to low math achievement, failure to enroll in advanced mathematics courses, and poor scores on standardized tests of math achievement. Math anxiety creates a focus of limited working memory on managing anxiety reaction rather than on solving the math problem, but it can be reduced by therapeutic interventions.”
How are you addressing the stress? Do you ever ask your students how they are feeling about the math? Do you teach them relaxation techniques? Teach them how to stop and simply take a deep breath and tell themselves they can do it. The report says we need to explore the idea of self-efficacy and its impact on learning math more. It notes that “self-efficacy (i.e., the belief that one has the specific skills needed to be successful, which differs from self-esteem)” can impact a students engagement, persistence and confidence in math class.
Happy Mathing,
Dr. Nicki
http://www2.ed.gov/about/bdscomm/list/mathpanel/report/learning-processes.pdf
Read Full Post | Make a Comment ( 2 so far )Breaking down the National Math Report: Implications for the Whole Class and Small Guided Math Groups
I am always talking about the National Mathematics Advisory Panel Report because it is really important. It will inform policy for the next decade. So, I have decided to do a series of salient points from the report.
The Math Report says that fluency with whole numbers is important. It stresses that children should have a ROBUST SENSE OF NUMBER by the end of grade school.
Here are some highlights (which by the way are now addressed in the Common Core):
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Understand Place value,
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Have the Ability to compose and decompose whole numbers
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Understanding basic operations of addition, subtraction, multiplication and division
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Understanding use of commutative, associative and distributive properties
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Computing efficiently
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Knowing how to problem solve.
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Automaticity with their basic facts of addition, subtraction, multiplication and division.
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Fluency in standard algorithms and be able to estimate.
WHERE ARE THE CHILDREN IN YOUR SCHOOL AT ALONG THIS CONTINUUM? WHAT DO THEY DO REALLY WELL AND WHAT IS LACKING? HOW DO YOU FIX IT? WHAT IS YOUR SCHOOL CURRENTLY EMPHASIZING? What’s the action plan to develop a ROBUST SENSE OF NUMBER among ALL CHILDREN at your school?
I like that phrase “Robust Sense of Number.” It gives us somewhere to go, somewhere to head…
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( None so far )April 22nd is National Jelly Bean Day
Here are some great math links to help you celebrate National Jelly Bean Day!
Jelly Bean Graph Ideas (Click the Jelly Bean Graph but Be Sure to LABEL IT!)
Jelly Bean Estimation (Create a real station in your class.)
Even More Jelly Bean Estimation
Powers of Ten (Be sure to click on the Jelly Bean and watch what happens!)
More Jelly Bean Math (Measurement)
Upper Elementary and Middle School Jelly Bean Math
Extra
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( 1 so far )During April Keep a Math Poem in Your Pocket! Money Poems
Some great money poems!
Resource 2 (scroll down to the money poems)
Lessons for Shel Silverstein’s Money Poem: Smart (listen to it on public radio)
Resource 4 (great video of kids acting out poem)
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( 2 so far )April is Poetry Month: Great Math Poetry Activity Links
Here is a great site: http://mathstory.com/Poems/mathpoemspage.html (be sure to read the ones about the numerator and the denominator dogs; also read the one about the trapezoid and the one about Perimeter Paul; there are plenty of others too! Enjoy.)
Happy Mathing,
Dr. Nicki
Read Full Post | Make a Comment ( 1 so far )Sesame Street Math Games: Great for Math Centers
Here are 5 great Sesame Street math games!
Mixed Skills (Counting and Measurement)
Go here (Numbers and Counting Games) to find more Sesame Math Fun!
Happy Mathing,
Dr. Nicki
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Dr. Nicki's Guided Math Blog 
