Leveraging Dynamic and Dependable Spreadsheets Focusing on Algebraic Thinking and Reasoning

2015 ◽  
pp. 1-23
Author(s):  
Margaret L. Niess
Keyword(s):  
Middle Grades ◽  
Mathematics Learning ◽  
State Standards ◽  
Algebraic Thinking ◽  
Learning Tools ◽  
Mathematics Problems ◽  
Mathematical Problems ◽  
The Common ◽  
Linear Problems ◽  
Formal Algebra

Algebraic thinking and reasoning are important skills for students to develop as they transition from arithmetic to algebra. The Common Core State Standards for Mathematics links these ideas through their mathematical practices where students make sense of mathematical problems, reason abstractly, model with mathematics, and use appropriate tools that engage them in algebraic thinking and reasoning. This chapter focuses on how a specific tool—the spreadsheet—supports students in building their understandings of spreadsheet features and capabilities while also engaging them in thinking more logically about numbers as needed in preparation for formal algebra. The challenge for teachers is to scaffold students' learning about and with spreadsheets as mathematics learning tools for exploring patterns, variables, and linear problems. This chapter describes this transition through multiple problems where students learn to design dynamic and dependable spreadsheets in ways that concurrently develop their algebraic reasoning and thinking through middle grades mathematics problems.

Learning Disabilities in Mathematics

2017 ◽  
Author(s):  
Carleen Franz ◽  
Lee Ascherman ◽  
Julia Shaftel
Keyword(s):  
Common Core State Standards ◽  
Mathematics Curriculum ◽  
Mathematics Learning ◽  
Number System ◽  
State Standards ◽  
Learning Disorder ◽  
Core State ◽  
Mathematics Problems ◽  
The Common ◽  
Mathematics Disabilities

This chapter illustrates the complexity of the mathematics curriculum and why students who struggle to comprehend mathematics face additional challenges in terms of remedial instruction. Mathematics disabilities are more common than often believed. These difficulties frequently stem from a deficit in basic numeracy, or an understanding of how numbers work and how our number system operates. A breakdown of mathematics concept areas from the Common Core State Standards illustrates the breadth of mathematics content. Case studies exemplify various presentations of mathematics disorders. Mathematics problems may remain undercover longer than other types of disabilities, and identification of a mathematics learning disorder may not occur until college. Assessment and remedial techniques are included.

Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets

2013 ◽  
pp. 228-233
Author(s):  
Ayhan Kursat Erbas ◽  
Sarah Ledford ◽  
Chandra Hawley Orrill ◽  
Drew Polly
Keyword(s):  
Middle School ◽  
Common Core State Standards ◽  
Middle Grades ◽  
Mathematical Thinking ◽  
State Standards ◽  
Educational Technologies ◽  
Core State ◽  
Geometric Patterns ◽  
The Common ◽  
Support Students

As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between numbers has gained more importance. Specifically, students’ conceptual understanding of numerical patterns is critical in middle school, as it lays a groundwork for fostering mathematical thinking at all levels. Educational technologies can enhance student’s explorations of patterns by providing opportunities to represent patterns, test conjectures, and make generalizations. In this chapter, the authors illustrate how spreadsheets can support students’ explorations of both arithmetic and geometric patterns in the middle grades.

scholarly journals Development of Mathematics Learning Devices Based on Guided Discovery Learning Models and Focusing on Students’ Mathematical Power at SMP Istiqlal Delitua

2021 ◽  
Vol 4 (1) ◽  
pp. 50-62
Author(s):  
Julian A. Hartono ◽  
Ida Karnasih ◽  
Dian Armanto
Keyword(s):  
Mathematics Learning ◽  
Discovery Learning ◽  
Test Reliability ◽  
Average Level ◽  
Learning Tools ◽  
Guided Discovery ◽  
Ability Test ◽  
Average Value ◽  
Mathematical Problems ◽  
Quantitative Descriptive

This developmental research aimed to analyze the validity of learning devices, practicality and effectiveness of the devices, as well as student responses to the use of Guided Discovery learning based learning devices that focusing on Mathematical Power. Data collecting was done by using a validation questionnaire with the observation method, a control problem ability test with mathematical power, and student questionnaire responses to guided discovery-based learning tools. Data analysis used qualitative and quantitative descriptive techniques. Testing of research instruments was carried out at SMP Istiqlal Delitua. The results of the analysis of the validity of the equipment showed that the total equipment was declared valid with an average level of validity of 4, 73 very good criteria. The result of the practicality test showed that the device was stated to be very practical with the proportion of practicality level of 89.94%. To test the effectiveness that the learning device was declared effective with the proportion of effectiveness of 86.49%, with Minimum Completeness Criteria achieved 89.29% of students completed, and 10.17% of students not completed. Learning objectives are achieved with the average level of achievement of goals was 88.13%, and students' responses to the feasibility of the devices getting an average total presentation of 94.9% with very good criteria. The results of the test of the ability of mathematical problems obtained an average value of 79.00 with a good predicate and a standard deviation of 9.76, and the test reliability coefficient of 0.5714 in the moderate category. Thus it can be concluded the Guided Discovery Learning device was valid, practical, and effective, and the student's response to the appropriateness of the device was in very good criteria.

scholarly journals Pengembangan Desain Pembelajaran Matematika Berbantuan Aplikasi GeoEnzo untuk Menumbuhkan Kemampuan Metakognitif Siswa SMK Mega Link Majene

2021 ◽  
Vol 17 (2) ◽  
pp. 115
Author(s):  
Syamsuddin Syamsuddin ◽  
Herlina Ahmad
Keyword(s):  
Design Research ◽  
Mathematics Learning ◽  
Three Dimensional ◽  
Student Response ◽  
Initial Assessment ◽  
Design Stage ◽  
Learning Tools ◽  
Mathematical Concepts ◽  
Mathematical Problems ◽  
Metacognitive Abilities

Covid-19 is affecting the world of education. Teachers are intended to change the paradigm of teaching methods, teachers face digital habits. The application of learning applications is an option in instilling mathematical concepts. The application of learning mathematics is one of the media that can be used by teachers in growing students' metacognitive abilities in understanding and solving mathematical problems. This type of research is a design research using the Plomp model with five stages, including: (1) initial assessment stage (2) design stage, (3) realization/construction stage, (4) test, evaluation and revision stage, and (5) stage implementation. This study aims to design three-dimensional learning assisted by the GeoEnzo application to foster students' metacognitive abilities in understanding and solving mathematical problems, especially three-dimensional material. The subjects of this study were students of class XII SMK Mega Link Majene which opened 40 people. This research resulted in: (1) the development of mathematical learning tools, especially on three-dimensional material that was valid, practical, and effective; (2) student activity observation sheets and teacher implementation; (3) student response questionnaires; and (4) learning outcomes test. The results of the research on the development of the GeoEnzo-assisted mathematics learning design are valid, practical, and effective for improving the metacognitive abilities of the students of SMK Mega Link Majene. 

scholarly journals PENINGKATAN KEMAMPUAN GURU DALAM MENGEMBANGKAN RANCANGAN PERMASALAHAN MATEMATIKA DITINJAU DARI LEVEL KEMAMPUAN BERPIKIR SISWA

2019 ◽  
Vol 4 (1) ◽  
pp. 49-68
Author(s):  
Baiq Rika Ayu Febrilia ◽  
Eliska Juliangkary
Keyword(s):  
Junior High School ◽  
Mathematics Learning ◽  
Thinking Skills ◽  
Design Problems ◽  
Mathematics Problems ◽  
Before And After ◽  
Mathematical Problems ◽  
Qualitative Descriptive ◽  
Level Of Thinking ◽  
Level Of Understanding

The ability of a teacher to design mathematical problems affects the characteristics and quality of mathematics learning that teachers do in class. Therefore, teachers need to have insight into how to design problems to encourage certain students' thinking skills. This study aims to describe improvement in teacher's ability to design mathematics problems before and after discussion activities designed by researchers. The method used is qualitative descriptive with the subject of seven junior high school mathematics teachers. Based on the results of this study it was found that after participating in the discussion activities, the number of teachers who designed problems that could encourage the level of thinking ability to apply decreased by 28.57%, the level of evaluation increased by 21.43%, the level analyzed remained, and the level of understanding increased by 7.14%. From 28 problems that have been designed both before and after the discussion activities, it is found that 10.71% is a matter that drives the level of understanding, 50% encourages the level of application, 17.86% encourages the level of analysis and 21.43% encourages the level to evaluate.

The iPad

2015 ◽  
pp. 128-137
Author(s):  
Sandra Alon ◽  
Heejung An ◽  
David Fuentes
Keyword(s):  
Common Core ◽  
Common Core State Standards ◽  
Conceptual Learning ◽  
State Standards ◽  
Learning Tools ◽  
Core State ◽  
The Common

This chapter discusses the technology vision of the Common Core State Standards (CCSS) and shares guidelines for choosing apps that are most appropriate to meet those objectives. Towards this end, a specific rubric for evaluating the effectiveness of different apps is presented. Advantages of existing apps that can be incorporated into iPad instruction to enhance conceptual learning and drill mathematics processes are reviewed. Common disadvantages of existing apps are also highlighted. Specific examples of how to make the use of the iPad most efficient and avoid common pitfalls of some purported learning tools are also discussed. The chapter concludes with areas still in need of further research.

Measuring Tangrams on a Geoboard

2017 ◽  
Vol 22 (6) ◽  
pp. 374-378
Author(s):  
Carol J. Bell
Keyword(s):  
Common Core ◽  
Common Core State Standards ◽  
State Standards ◽  
Algebraic Thinking ◽  
Plane Geometry ◽  
Core State ◽  
The Common ◽  
Basic Concepts

many of us are familiar with the tangram and the geoboard. A tangram is a dissection puzzle consisting of seven flat shapes. One objective of the puzzle is to form a specified shape using all seven pieces, with no pieces overlapping. Geoboards are generally used to explore basic concepts found in plane geometry, such as perimeter and area, or basic shapes, such as polygons. Using tangrams in combination with a geoboard provides a rich activity for students that will help them further develop their skills and understanding of operations and algebraic thinking, number and operations, measurement, and geometry, also mentioned in the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010).

scholarly journals Mathematical Representation of Students in Solving Mathematic Problems Reviewed from Extrovert-Introvert Personality

2021 ◽  
Vol 5 (2) ◽  
pp. 323
Author(s):  
Aulia Ar Rakhman Awaludin ◽  
Noni Selvia ◽  
Finata Rastic Andrari
Keyword(s):  
Problem Solving ◽  
Mathematics Learning ◽  
Sampling Technique ◽  
Personality Types ◽  
Algebraic Thinking ◽  
Mathematical Representation ◽  
Research Subjects ◽  
Mathematical Problems ◽  
Multistage Sampling ◽  
Almost All

In implementing mathematics learning in schools, educators must pay attention to five main competencies, namely problem solving, communication, connection, reasoning, and representation. Mathematical representation is a tool to convey students' algebraic thinking as an aid to construct their ideas about patterns and functions. This study aims to examine the mathematical representation of students in terms of introvert and extrovert personality types. To see the characteristics of mathematical representations in solving mathematical problems when viewed from the personality type of each student. This research method is descriptive qualitative. The number of schools and students who were sampled from this study was taken using a multistage sampling technique. The data collection instruments in this study were personality questionnaires, problem-solving tests, interviews, observations, and documents obtained from research subjects. The problem-solving analysis used is based on the Krulik and Rudnik steps. The personality types of extroverted students and introverted students do have different mindsets so that even though in some steps they use the same representation, their tendencies or habits represent problem-solving using different forms of representation. The personality types of extroverted students represent them more symbolically and almost all answers from extroverted students are closer to true when compared to introverted students.

scholarly journals Development of Mathematic Learning Devices Through The Application of The Problem Based Learning Model to Facilitate KPMM in Number Pattern Materials

2021 ◽  
Vol 5 (2) ◽  
pp. 267
Author(s):  
Eko Payasto ◽  
Maimunah Maimunah ◽  
Sehatta Saragih
Keyword(s):  
Lesson Plan ◽  
Mathematics Learning ◽  
Problem Based Learning ◽  
Student Response ◽  
Small Scale ◽  
Learning Tools ◽  
Model Learning ◽  
Average Percentage ◽  
Number Pattern ◽  
Mathematical Problems

This research is motivated by the low ability of students to solve mathematical problems (KPMM) and the teacher has not been optimal in developing mathematics learning tools independently. The purpose of this study was to produce mathematics learning tools through the application of the Problem Based Learning (PBL) model to facilitate KPMM students of SMP Negeri 2 Pangkalan Lesung on number pattern material. This type of research is development research using the 4-D model. Learning tools developed in the form of syllabus, lesson plan (RPP) and student worksheets (LKPD) and KPMM questions. The instruments in this study were validation sheets and student questionnaires. Validation sheets consist of syllabus validation sheets, lesson plans validation sheets, and student worksheet validation sheets, while student questionnaires are in the form of student response sheets. Based on the results of the validation analysis, it shows that the device being developed is very valid. The result of the validation of the syllabus was 3.79; the average RPP score was 3.67; and the average LKPD score was 3.66. The student response questionnaire on the small-scale test showed an average percentage of 94.67% with the very practical category. The learning tools developed were valid and practical for use by students of SMPN 2 Pangkalan Lesung.

The iPad

2018 ◽  
pp. 377-386
Author(s):  
Sandra Alon ◽  
Heejung An ◽  
David Fuentes
Keyword(s):  
Common Core ◽  
Common Core State Standards ◽  
Conceptual Learning ◽  
State Standards ◽  
Learning Tools ◽  
Core State ◽  
The Common

This chapter discusses the technology vision of the Common Core State Standards (CCSS) and shares guidelines for choosing apps that are most appropriate to meet those objectives. Towards this end, a specific rubric for evaluating the effectiveness of different apps is presented. Advantages of existing apps that can be incorporated into iPad instruction to enhance conceptual learning and drill mathematics processes are reviewed. Common disadvantages of existing apps are also highlighted. Specific examples of how to make the use of the iPad most efficient and avoid common pitfalls of some purported learning tools are also discussed. The chapter concludes with areas still in need of further research.

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