Math in NEISD. Helping students uncover math, not just cover it.
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Helping students uncover math, not just cover it.
“Knowing mathematics means being able to use it in purposeful ways. Mathematical ability comes from being taught math so that understanding is emphasized, ideas are explored, alternate methods are encouraged and the purpose for what is being done is always evident.”
- Marilyn Burns
Depth of UnderstandingReasoningPurposeCommunication
Mathematics is something to be deeply understood so that it can be used effectively
“We have a long history of evidence that when children are not taught for conceptual understanding – when they learn mathematical ideas simply through memorizing rules or practicing abstract procedures they do not understand – a breakdown comes when they are unable to put mathematics to work to solve problems.”
Understanding takes time.
Ruth E. Parker, Mathematics Education Collaborative p. 23
How are the traditional strategies that we were taught in elementary school different from how we solve problems in our everyday lives?
“Accuracy denotes the ability to produce an accurate answer : efficiency refers to the ability to choose an appropriate, expedient strategy for a specific computation problem: and flexibility means the ability to use number relationships with ease in computation”
After decades of good intentions with standard algorithms, far too many students do not understand the concepts that support them.
Errors with invented strategies are less frequent and almost never systemic.
Time-consuming struggle in the early stages results in ideas that are meaningful and well integrated in a web of ideas that are robust and long lasting.
2 x 16 =
8 x 5 =
8 x 10 =
8 x 6 =
8 x 16 =
4 x 5 =
4 x 10 =
4 x 50 =
4 x 49 =
Those who become adept with non-standard methods will consistently perform computations more quickly than those using a traditional algorithm.
Arrays are useful for solving for solving and visualizing multi-digit multiplication problems.
Students use rectangular arrays to represent the relationship between a number and its factors: the area of an array is the number, and the length and width are one pair of the factors.
“Perhaps the most important feature of learning with understanding is that such learning is generative. When students acquire knowledge with understanding, they can apply that knowledge to learn new topics and solve new and unfamiliar problems.”
Carpenter and Lehrer 1999
What can you do when your child is frustrated and doesn’t know what to do?
You can bring mathematics in your home through play that helps your child practice basic skills within engaging and challenging contexts.
Encourage your child when he or she is frustrated by a math problem, making sure that your words and actions model a belief that mathematics is important and that you value your child’s persistence in working on challenging math problems.
“It is important to remember that we all climb hills differently. We take different paths, different steps, and different journeys. We reach landmarks in different ways and different times.
If we push or pull children up a hill and make them practice our steps, our ways, or, worse yet, drop them by helicopter at points on the journey without the climb of getting there, we may get them up the mountain-but they won’t own it. They may reach the vista, but they won’t feel empowered by the climb. They won’t take on the next hill or journey.
And most important, they won’t have learned to climb, how to mathematize their own lived worlds. If, however, we support their steps, work with them as young mathematicians, the climbs, the vistas, and the joys of the journey will be theirs forever.”
Young Mathematicians at Work
Students in standards-based programs consistently outperform their traditional counterparts on measures of understanding and problem solving