Mathematics

In the second grade we use the math program called Investigations as the foundation for our math instruction.  It is a comprehensive hands-on activity program that meets the standards established by the National Council of the Teachers of Mathematics.
 

Goals & Guiding Principles

Investigations in Number, Data, and Space is a mathematics curriculum designed to engage students in the making sense of mathematical ideas. The curriculum has six major goals:
•    Support students to make sense of mathematics and learn that they can be mathematical thinkers.
•    Focus on computational fluency with whole numbers as a major goal of the elementary grades.
•    Provide substantive work in important areas of mathematics - rational numbers, geometry, measurement, data, and early algebra - and connections among them.
•    Emphasize reasoning about mathematical ideas.
•    Communicate mathematics content and pedagogy to teachers.
•    Engage the range of learners in understanding mathematics.
 

Grade 2 Curriculum Units

•    Counting, Coins and Combinations - Addition, Subtraction and the Number System 1
•    Shapes, Blocks, and Symmetry - 2-D & 3-D geometry
•    Stickers, Number Strings, and Story Problems - Addition, Subtraction and the Number System 2
•    Pockets, Teeth, and Favorite Things - Data Analysis
•    How Many Floors? How Many Rooms? - Patterns, Functions, and Change
•    How Many Tens? How Many Ones? - Addition, Subtraction and the Number System 3
•    Parts of a Whole, Parts of a Group - Fractions
•    Partners, Teams, and Paper Clips - Addition, Subtraction and the Number System 4
•    Measuring Length & Time - Measurement

Along with the Investigations curriculum, we will also be using First Steps in Mathematics, a series of teacher resource books to help diagnose, plan, implement and judge the effectiveness of the learning experiences provided for the students.

Learning Mathematics (from First Steps in Mathematics 2004)
Learning is Built on Existing Knowledge - Learners’ interpretations of mathematical experiences depend on what they already know and understand. Students’ existing knowledge should be recognized and used as the basis for further learning.

Learning Requires That Existing Ideas Be Challenged - Learning requires that students extend or alter what they know as a result of their knowledge being challenged or stretched in some way. The students must find some way of dealing with the challenge or conflict provided by the new information in order to learn.

Learning Occurs when the Leaner Makes Sense of New Ideas - Teaching is important - but learning is done by the learner rather than to the learner. This means the learner acts on and makes sense of new information. Students almost always try to do this. However, in trying to make sense of their mathematical experiences, some students will draw conclusions that are not quite what their teachers expect. Also, when students face mathematical situations that are not meaningful, or are well beyond their current experiences and reach, they often conclude that the mathematics does not make sense of that they are incapable of making sense of it. This may encourage students to resort to learning strategies based on the rote imitation of procedures. The result is likely to be short-term rather than effective long-term learning. Teachers have to provide learning experiences that are meaningful and challenging, but within the reach of their students.
 

Learning Involves Taking Risks and Making Errors - In order to learn, students have to be willing to try a new or different way of doing things, and stretch a bit further than they think they can. At times, mistakes can be a sign of progress as students are trying to generalize patterns and make sense of new ideas. Errors can provide a useful source of  feedback, challenging students to adjust their conceptions before trying again. Errors may also suggest that learners are prepared to work on new or difficult problems where increased error is likely. Or, they may try improved ways of doing things that mean giving up old and safe, but limited strategies.
Learners Get Better with Practice - Students should get ample opportunity to practice mathematics, but this involves much more than the rote or routine repetition of facts and procedures. Likewise, if students are to develop good mental arithmetic, they will need spaced and varied practice with a repertoire of alternative addition strategies and with choosing among them. Extensive repetitive practice on a single written addition algorithm is unlikely to help with this, In fact, it is more likely to interfere with it.
 

Learning is Helped by Clarity of Purpose for Students as well as Teachers - Learning is likely to be enhanced if students understand what kind of learning activity they should be engaged in at any particular time. This means helping students to distinguish between tasks that provide practice of an already learned procedure and tasks that are intended to develop understanding of mathematical concepts and processes. In the former case, little that is new is involved, and tasks are repetitive, so they become habitual and almost unthinking. With tasks that are intended to develop understanding, non-routine tasks and ideas may be involved. Students may spend a considerable amount of time on a single task. They should recognize that, for such activities, persistence, thoughtfulness, struggle and reflection are expected.