Facilitating Mathematical Practices through Visual Representations

2017 ◽  
Vol 23 (7) ◽  
pp. 404-412
Author(s):  
Aki Murata ◽  
Chana Stewart
Keyword(s):  
First Graders ◽  
Visual Representations ◽  
Place Value ◽  
Mathematical Practices ◽  
Number Lines ◽  
Practice Standards

This set of lesson examples demonstrates effective uses of magnets, number lines, and ten-frames to implement practice standards as first graders use place value to solve addition problems.

Using a Base-Ten Blocks Learning/Teaching Approach for First- and Second-Grade Place-Value and Multidigit Addition and Subtraction

1990 ◽  
Vol 21 (3) ◽  
pp. 180-206 ◽  
Author(s):  
Karen C. Fuson ◽  
Diane J. Briars
Keyword(s):  
School District ◽  
First Graders ◽  
Second Graders ◽  
Teaching Approach ◽  
Second Grade ◽  
Place Value ◽  
Urban School District ◽  
Value System ◽  
Number Words ◽  
Addition And Subtraction

A learning/teaching approach used base-ten blocks to embody the English named-value system of number words and digit cards to embody the positional base-ten system of numeration. Steps in addition and subtraction of four-digit numbers were motivated by the size of the blocks and then were carried out with the blocks; each step was immediately recorded with base-ten numerals. Children practiced multidigit problems of from five to eight places after they could successfully add or subtract smaller problems without using the blocks. In Study 1 six of the eight classes of first and second graders (N=169) demonstrated meaningful multidigit addition and place-value concepts up to at least four-digit numbers; average-achieving first graders showed more limited understanding. Three classes of second graders (N=75) completed the initial subtraction learning and demonstrated meaningful subtraction concepts. In Study 2 most second graders in 42 participating classes (N=783) in a large urban school district learned at least four-digit addition, and many children in the 35 classes (N=707) completing subtraction work learned at least four-digit subtraction.

A Teacher's Journal: Opportunities to Develop Place Value through Student Dialogue

2003 ◽  
Vol 10 (2) ◽  
pp. 78-82
Author(s):  
Amy R. Kari ◽  
Catherine B. Anderson
Keyword(s):  
Facial Expressions ◽  
First Graders ◽  
Second Graders ◽  
Place Value ◽  
Student Dialogue ◽  
Paper And Pencil

The problem 11 + 9 was written on the board at the front of the room. Eleven first graders and nine second graders sat on the carpet, their facial expressions intent as they thought about solutions. I had asked them to try to think of strategies they could use that did not involve counting on their fingers. They did not use paper and pencil because this was what we call “Mental Math” time at our school.

Reasoning and Working Proportionally with Percent

2004 ◽  
Vol 9 (6) ◽  
pp. 326-330
Author(s):  
Melanie Parker
Keyword(s):  
High School ◽  
Middle School ◽  
Junior High School ◽  
Visual Representations ◽  
School Curriculum ◽  
High School Curriculum ◽  
Visual Models ◽  
The Everyday ◽  
Number Lines ◽  
The Right

Percent, an important topic in the middle school and junior high school curriculum, is commonly found in the everyday lives of students. This topic presents a wonderful opportunity for students to reason and work proportionally with quantities. Teachers have tried different instructional approaches with varying degrees of success, but percent remains a difficult topic for students to understand. Various representations have been used in instruction, such as fractions, decimals, pie charts, and number lines. Although the use of visual models is a step in the right direction, these visual representations are often abandoned as students progress into the topic. Emphasis is then placed on conversions, equations, and computations. However, these representations may not stress the very nature of the concept. Instruction in this important topic should stress what percent really is instead of concentrating on surface features of the numeral and the problems in which it appears.

How Huge Is a Hundred?

1999 ◽  
Vol 6 (3) ◽  
pp. 154-159
Author(s):  
Susan Hampton Auriemma
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Learning Environment ◽  
Number Sense ◽  
First Graders ◽  
School Mathematics ◽  
Place Value ◽  
Important Goal ◽  
Evaluation Standards ◽  
And Mathematics

How much is a hundred?” How would your students respond to such a question? This article shares the experiences of my first graders as they participated in activities that develop number sense to answer this question. Teaching number sense to students in grades K–4 is an important goal of the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989). The following activities are based on the Standards in many ways. They require problem solving, reasoning, communicating, and connecting mathematics to everyday situations that interest children. They provide opportunities to develop measurement and place-value concepts and to integrate reading, writing, drawing, and mathematics in ways that contribute to a cooperative learning environment.

Examining First-Graders’ Developing Understanding of Place Value via Base-Ten Virtual Manipulatives

2021 ◽  
Author(s):  
Lucia M. Flevares ◽  
Michelle Perry ◽  
Shereen Oca Beilstein ◽  
Neet Priya Bajwa
Keyword(s):  
First Graders ◽  
Virtual Manipulatives ◽  
Place Value

A Meta-Analytic Synthesis of Early Numeracy Interventions for Low-Perfoming Young Children

2020 ◽  
Author(s):  
Garyfalia Charitaki ◽  
Sotiria Tzivinikou ◽  
Garyfallia Stefanou ◽  
Spyridon - Georgios Soulis
Keyword(s):  
Instructional Strategies ◽  
First Graders ◽  
Explicit Instruction ◽  
Meta Analysis ◽  
Corrective Feedback ◽  
Visual Representations ◽  
Early Numeracy ◽  
Short Term ◽  
Substantial Impact ◽  
Instructional Arrangement

Early numeracy is related to preschoolers’ acquisition of skills such as understanding and operating with quantities. Consequently, early numeracy has substantial impact on first Graders’ attainments in typical mathematics. Meta-analysis was conducted to address the extent in which early numeracy interventions are effective. Twenty studies were analyzed, including 3.080 young low-performing children (Ncontrol=1.815, Ntreatment=1.265). The overall best estimate for programs based on Early Numeracy Interventions odds ratio was moderately effective g=0.61 (95% CI=[0.44, 0.78]). Heterogeneity was large. Results of the final meta-regression model predicted larger treatment effects for short-term interventions including 1 to 9 sessions. On average, the interventions included instructional strategies such as Explicit Instruction (g=0.57), Corrective Feedback (g = 0.55), CRA (g =0.64), Concrete Manipulatives (g=0.60) Visual Representations (g=0.57) and one-to-one instructional arrangement g=0.79 are moderately effective for children aged 5-8. Results of the study are discussed with respect to implications for designing early numeracy interventions.

A Place-Value Game for First Graders: A Teacher-Made Device

1957 ◽  
Vol 4 (5) ◽  
pp. 217-218
Author(s):  
Irene R. MacRae
Keyword(s):  
First Graders ◽  
Primary Teachers ◽  
Place Value ◽  
Number Concepts ◽  
Small Children ◽  
Initial Learning

Many teachers find that place value is one of the more difficult number concepts to explain to small children. The following game was devised to help reinforce the understanding of place value after it has been introduced by the use of the Hundreds, Tens and Ones Chart. This chart is familiar to primary teachers. The game uses the same pocket device used in the chart. Thus children can reinforce their initial learning by practice under conditions similar to those in which the learning took place.

Memorial Consequences of Environmental Context Change in Children and Adults

2010 ◽  
Vol 57 (6) ◽  
pp. 455-461 ◽  
Author(s):  
Alp Aslan ◽  
Anuscheh Samenieh ◽  
Tobias Staudigl ◽  
Karl-Heinz T. Bäuml
Keyword(s):  
Elementary School ◽  
Young Adults ◽  
Episodic Memory ◽  
Middle Childhood ◽  
First Graders ◽  
Fourth Graders ◽  
Environmental Context ◽  
Context Change ◽  
Context Dependent

Changing environmental context during encoding can influence episodic memory. This study examined the memorial consequences of environmental context change in children. Kindergartners, first and fourth graders, and young adults studied two lists of items, either in the same room (no context change) or in two different rooms (context change), and subsequently were tested on the two lists in the room in which the second list was encoded. As expected, in adults, the context change impaired recall of the first list and improved recall of the second. Whereas fourth graders showed the same pattern of results as adults, in both kindergartners and first graders no memorial effects of the context change arose. The results indicate that the two effects of environmental context change develop contemporaneously over middle childhood and reach maturity at the end of the elementary school days. The findings are discussed in light of both retrieval-based and encoding-based accounts of context-dependent memory.

Sign in / Sign up

Export Citation Format

Share Document