By Kitty Rutherford, Posted April 27, 2015 –
People of all ages love to play games that are fun
and motivating. Games give students opportunities to explore fundamental number
concepts, such as the counting sequence, one-to-one correspondence, and computation
strategies. Engaging mathematical games can also encourage students to explore
number combinations, place value, patterns, and other important mathematical
concepts. Further, they afford opportunities for students to deepen their
mathematical understanding and reasoning. Teachers should provide repeated
opportunities for students to play games, then let the mathematical ideas
emerge as students notice new patterns, relationships, and strategies. Games
are an important tool for learning in elementary school mathematics classrooms:
• Playing games
encourages strategic mathematical thinking as students find different
strategies for solving problems and deepen their understanding of numbers.
• When played
repeatedly, games support students’ development of computational fluency.
• Games present opportunities
for practice, often without the need for teachers to provide the problems. Teachers
can then observe or assess students and work with individuals or small groups
of students.
• Games have the
potential to allow students to develop familiarity with the number system and
with “benchmark numbers” (such as 10s, 100s, and 1000s) and engage in computation
practice, building a deeper understanding of operations.
• Games support a
school-to-home connection. Parents can learn about their children’s
mathematical thinking by playing games with them at home.
This game is on p. 65 of the downloadablePDF.
Building Fluency
Fluency
requires a balance and connection between conceptual understanding and
computational proficiency. Computational methods that are over-practiced
without understanding are forgotten or remembered incorrectly. Conceptual
understanding without fluency can inhibit the problem-solving process (NCTM
2000, Principles and Standards for School Mathematics, p. 35).
Developing
computational fluency is an expectation of the Common Core State Standards for
Mathematics. Games provide opportunity for meaningful practice. The research
about how students develop fact mastery indicates that drill techniques and
timed tests do not have the power that mathematical games and other experiences
have. Appropriate mathematical activities are essential building blocks to
develop mathematically proficient students who demonstrate computational
fluency (Van de Walle and Lovin, Teaching Student-Centered Mathematics
Grades K–3, p. 94). Remember, computational fluency includes efficiency,
accuracy, and flexibility with strategies (Russell 2000).
The
kinds of experiences that teachers
offer their students clearly play a major role in determining the extent and
quality of students’ learning. Students can build understanding by actively
engaging in tasks and experiences designed to deepen and connect their knowledge. Procedural fluency and
conceptual understanding can be developed through problem solving, reasoning,
and argumentation (NCTM 2000, Principles and Standards for School
Mathematics, p. 21). Meaningful practice is necessary to develop
fluency with basic number combinations and strategies with multidigit numbers. Practice
should be purposeful
and should focus on developing thinking strategies and a knowledge of number relationships rather
than on drilling isolated facts (NCTM 2000, Principles and Standards for
School Mathematics, p. 87). Do not subject any student to computation
drills unless the student has developed an efficient strategy for the facts
included in the drill (Van de Walle and Lovin 2006, Teaching
Student-Centered Mathematics Grades K–3, p. 117). Drills can strengthen
strategies with which students feel comfortable—those they
“own”—and will help make these strategies increasingly automatic. Therefore, strategy
drills will allow students increasing efficiency, even to the point of
recalling a fact without being conscious of using a strategy. Drills without an
efficient strategy offer no assistance (Van de Walle and Lovin 2006, Teaching
Student-Centered Mathematics Grades K–3, p. 117).
This game is on p. 5 of the downloadable
PDF.
Cautions
Sometimes
teachers use games solely to practice number facts. These games usually do not
engage children for long because they are based on students’ recall or
memorization of facts. Some students are quick to memorize; others need a few
moments to compute a related fact. When students are placed in situations in
which recall speed determines success, they may infer that being “smart” in
mathematics means getting the correct answer quickly instead of valuing the
process of thinking. Consequently, students may feel incompetent when they use
number patterns or related facts to arrive at a solution and may begin to
dislike mathematics because they are not fast enough.
This game is on p. 67 of the downloadable PDF.
Introduce a game
A
good way to introduce a game to the class is for the teacher to play the game against
the class. After briefly explaining the rules, ask students to make the class’s
next move. Teachers may also want to model their strategy by talking aloud for
students to hear his or her thinking. “I placed my game marker on the six because
that would give me the largest number.”
Games
are fun and can create a context for developing students’ mathematical
reasoning. Through playing and analyzing games, students also develop their computational
fluency by examining strategies that are more efficient and by discussing
relationships among numbers. Teachers can create opportunities for students to
explore mathematical ideas by planning questions that prompt students to reflect
about their reasoning and make predictions. Remember to always vary or modify
the game to meet the needs of your leaners. Encourage the use of the Common
Core’s Standards for Mathematical Practice.
Holding Students Accountable
While
playing games, have students record mathematical equations or representations
of the mathematical tasks. This yields data for students and teachers to
revisit to examine their mathematical understanding.
After
playing a game, have students reflect on the game by asking them to discuss
questions orally or write about them in a mathematics notebook or journal:
• What skill did
you review and practice?
• Which strategies
did you use while playing the game?
• If you were to
play the games a second time, what different strategies would you use to be
more successful?
• How could you tweak or modify the
game to make it more challenging?
This game is on p. 42 of the downloadable PDF.
K–Grade 5 Math Games were
created by North Carolina teachers and can be accessed on the North Carolina
Department of Public Instruction,
under Kindergarten Instructional Resources/Games.
For
students to become fluent in arithmetic computation, “they must have efficient
and accurate methods that are supported by an under-standing of numbers and
operations. ‘Standard’ algorithms for arithmetic computation are one means of
achieving this fluency” (NCTM 2000, Principles and Standards for School
Mathematics, p. 35).
“Overemphasizing
fast fact recall at the expense of problem solving and conceptual experiences
gives students a distorted idea of the nature of mathematics and of their
ability to do mathematics” (Seeley 2009,
Faster Isn’t Smarter: Messages about Math, Teaching, and Learning in the 21st
Century, p. 95).
“Fluency refers to having efficient, accurate, and
generalizable methods (algorithms) for computing that are based on
well-understood properties and number relationships” [emphasis mine] (NCTM
2000, Principles and Standards for School Mathematics, p. 144).
“Computational fluency refers to having efficient and accurate methods
for computing. Students exhibit computational fluency when they demonstrate flexibility in the
computational methods they choose, understand
and can explain these methods, and produce accurate answers efficiently” [emphasis mine] (NCTM 2000, Principles
and Standards for School Mathematics, p. 152).
Kitty
Rutherford serves as the North Carolina Elementary Mathematics Consultant for
the Department of Public Instruction in Raleigh. She is an experienced leader,
collaborator, and licensed educator with a Master’s Degree in Elementary
Education coupled with over twenty-seven years’ experience teaching elementary school
students, training educators, collaborating with multiple stake-holders, and
implementing effective programs. She has received such honors as the
Presidential Award for Excellence in Mathematics and Science Teaching, NCCTM
Outstanding Elementary Mathematic Teacher, Alpha Delta Kappa State Excellence
in Education Award, and Teacher of the Year Finalist. She currently serves as
the State Coordinator for the NC Presidential Award for Excellence in
Mathematics Teaching and on the board of the North Carolina Council of Teachers
of Mathematics.