How will my child learn basic facts?
Knowing addition and multiplication facts is important, and your child will learn them in elementary school. The way in which your child will learn them differs from the drill and practice many adults remember. Research (Hasselbring, Goinn & Sherwood, 1986; Woodward, 2006) indicates drill and practice are useful for improving speed of recall for facts already being recalled from memory but have no effect on facts not yet recalled. Thus, knowing which facts you can recall and which you still have to work on is important. In grades two and three, children will actually identify the facts they don’t yet recall and devise ways to study them.
Further research (Kameenui & Simmons, 1990) also indicates that learning and retention of facts are facilitated by learning them based on their relationships to one another. Games in kindergarten and grade one and direct instruction in grades two and three emphasize thinking about the relationships between facts. For example, in a grade one game a child might say, There were 6 (of 10) pennies that were heads last time and now there are 4 heads! So 6+4 is the same as 4+6. A grade two student might write, I know 7+7=14. 8+7 is one more so it must be 15.
How will my child learn algorithms?
One way to understand algorithms is as generalized procedures that will work for a class of problems or a class of numbers. Although most of us learned one procedure for each whole number operation, the algorithms taught in other countries or time periods may have differed in their notation. The important unifying characteristic of any whole number operation algorithm is that it is based on the properties of our base ten number system and the operation itself. The 2d ed. of Investigations not only teaches the algorithms for addition, subtraction and multiplication, it helps children analyze why each works.
The goal is not only to learn procedures, but to develop “computational fluency.” Fluency includes three inter-related ideas: efficiency, accuracy, and flexibility.
- Efficiency entails keeping track of your strategy and not getting caught up in too many steps or elaborate notation.
- Accuracy includes estimating and determining the reasonableness of an answer, double-checking results, securing knowledge of “facts” and important number relationships, and carefully recording.
- Flexibility requires knowledge of more than one approach to solve a particular kind of problem, so that an appropriate strategy is chosen and also so that one method can be used to solve a problem and another method to double-check results.
Fluency demands more of students than does memorization of a single procedure. Important mathematical procedures are based on connected ideas about fundamental mathematical relationships. As Ma (1999) says in her study of Chinese and American teaching of elementary mathematics, "Being able to calculate in multiple ways means that one has transcended the formality of the algorithm and reached the essence of the numerical operations -- the underlying mathematical ideas and principles. The reason that one problem can be solved in multiple ways is that mathematics does not consist of isolated rules, but connected ideas. Being able to and tending to solve a problem in more than one way, therefore, reveals the ability and the predilection to make connections between and among mathematical areas and topics (p. 112.)" For more information on how the Investigations materials approach whole number operations, visit their website at http://investigations.terc.edu/library/curric-math and click on the PDF files for "Addition and Subtraction" or "Multiplication and Division".
How can I help my child?
The math games that make up part of the Investigations materials are a great way to practice facts and reasoning at the same time. Use the information in the family letters you will receive for each unit and the Student Math Handbook (grades one through four) to find other ways to engage in conversations at home about a topic being studied in school.
Use the Student Math Handbook and the resources listed below to find ways to ask questions that will stimulate your child’s reasoning and thinking about mathematics, rather than just asking your child to find the answer.
Participate in the family events around math at your school to learn more about the math content and ways in which your child is learning it.
Last, but most certainly not least, encourage your child to be persistent. We can all learn mathematics. If solutions elude you, formulate questions to ask the teacher. Good questions are essential to real learning.
Why is my child asked to write and talk about her solution or show her work?
We see communicating as a tool for learning. The act of clarifying, reflecting and articulating one’s thinking leads to deeper understanding and better retention. Mathematics is about thinking and abstraction. We want to support students in learning how to think about what they know in order to solve new problems and generate new ideas, as real mathematicians do. Talking something through or writing about it helps us to understand an idea in new or more extensive ways. In the 21st century more than memorized knowledge is required; children will need to be able to think and reason about what they know and communicate their ideas and understanding to others.
How will I know my child is appropriately challenged and/or supported in learning math?
The new math materials actually provide for great flexibility for teachers and students. Open-ended questions provide challenge and the use of concrete objects and visual models provide support. Many lessons actually contain suggestions for supporting or extending children’s learning. In this first year of implementation (2008-2009), all teachers K-2 (classroom and special education), district wide, will meet to plan each unit of study, including ways to meet the needs of all learners in each class.
Why does the homework have only one or two problems on it?
Investigations homework is based upon recent research on student success in mathematics. The purpose of assigning fewer problems is to encourage students to:
- work completely and thoughtfully.
- find several solutions to any given problem and refine their strategies, working toward efficiency in thinking and notation.
- use mathematical representations such as pictures, diagrams, graphs and tables.
- explain their thinking so someone would be able to replicate the solution.
- engage in math games that reinforce both concepts and skills.
Where can I find more information and resources about math?
Here are some links you may find helpful:
Check back often for new and updated information. You can e-mail specific questions to your child’s teacher and general questions about mathematics to Lisa Ultan, the District's professional developer for mathematics, at firstname.lastname@example.org.