Our Core Beliefs We believe that … 1. kids come first. 2. continuous improvement is critical for success of the Northwest Independent School District. 3. the success of each student is the shared responsibility of students, families, schools, and communities. 4. environment influences learning.
Solve It • What is the answer to 14 + 16. • Can you explain how you got that answer? • Can you find the answer in a different way?
Try It • Create two sticks of cubes. The first stick should have 14 cubes. The second stick should have 16 cubes. • How could you group cubes from the sticks to find the answer easier? • 4+6=10 • 10+10+10=30
Traditional Math • Collection of rules and procedures to memorize • Focus is on getting the “right” answer • Only one way to get the answer • Only some students are “good at math” John A. Van de Walle (2007)
How is the way we teach and learn mathematics different? Memorizing procedures to get an answer Do math in a way that makes sense to the learner Teacher – centered Student - centered
“The goal of mathematics should be toproduce learners who are both mathematically competentand confident. This does not come from merely memorizing rules and procedures, but from understanding relationships and knowing you can make sense of information and situations you encounter.”Ruth Parker (2000)
Why? • We are living in the Conceptual Age. • Employers want people who can apply what they learn and work collaboratively. • Traditional math does not work for all children. They don’t understand what they are learning. They just learn to do it because they are told.
Investigations in Number, Data, and Space • K-5 program • The middle school programs follows the same instructional model. • Focuses on mathematical thinking and reasoning.
Investigations in Number, Data, and Space • Teaches that there is still one correct answer. There are just many ways to prove the answer is correct. • Does not abandon traditional learning, just builds a conceptual understanding FIRST.
As a result of their everyday learning, students will…. Represent their thinking using models, words and numbers Explore problems in depth Make connections between mathematical ideas Develop fluency – efficiency, accuracy, and flexibility Develop problem-solving strategies Explain their thinking Choose a variety of tools and technology Find more than one way to solve a problem Learn with and through each other
Try It • Using the snap cubes at your table, try solving this problem through modeling: • 28-15
Memorizing Facts • 4 x 9=36 • Turn to a neighbor and explain why 4x9=36. • Learning your facts is an important skill that will be used in many more complex situations in future learning. The most important thing about understanding any operation is understanding why it works. That is our goal at Northwest ISD.
Understanding Why • 4x9=36 • Many students find this fact difficult to memorize. To help your child understand the problem, ask them to break it down into smaller (more manageable) parts.
Understanding Why • Multiplication problems can be represented in arrays… • 4 rows by 9 columns=36 • Many people can remember facts better if they can imagine a picture.
Understanding Why • One way to understand a fact is to break this fact into smaller parts. • Take the 4x9 array card out of your bag. Use the other array cards in your bag to find a combination of facts that will completely cover your 4x9 card. • Share your facts with a neighbor. • How would that be written mathematically? • These facts can be used to remember the answer to 4x9.
12x8 • Take out the 12x8 array card. Use the other array cards in your bag to find a combination of facts that will completely cover your 12x8 card. • Share your facts with a neighbor. • How would that be written mathematically? • Any of these facts can be used to remember the answer to 12x8.
Connections to Future Learning • This style of thinking directly correlates to junior high and high school algebra. • Algebra is about understanding number properties and relationships. Investigations teaching directly supports that.
Ways to support your child… “One of the most significant things parents can do is to help their children understand the normalcy and the value of struggle in mathematics. Learning math ultimately comes down to one thing: the ability, and choice, to put one’s brain around a problem – to stare past the confusion, and struggle forward rather than flee.” S. Sutton (1998)
Resources • “Helping Your Child With Math” • Math Games to play at home • Family letters • Websites-Many teachers have a section on their websites with Parent Links.