scholarly journals Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving later

2017 ◽  
Vol 24 (6) ◽  
pp. 1922-1928 ◽  
Author(s):  
Jerome D. Hoover ◽  
Alice F. Healy
Keyword(s):  
Problem Solving ◽  
Algebraic Reasoning ◽  
Ball Problem

Algebraic Problem Solving in the Primary Grades

2003 ◽  
Vol 9 (8) ◽  
pp. 444-449
Author(s):  
Robert B. Femiano
Keyword(s):  
Problem Solving ◽  
First Graders ◽  
Primary Grade ◽  
Algebraic Reasoning ◽  
Abstract Form ◽  
Teaching Experiences ◽  
Algebraic Problem ◽  
Formal Level ◽  
Level Of Thinking ◽  
Logic Puzzle

You may be surprised to learn that most first graders can solve for x in such problems as 2x + 1 = 21. I know so because they do it in my classroom daily, just not in the abstract form of x's and y's. Even though primary-grade students may lack the formal level of thinking required to “efficiently” solve equations, algebraic reasoning is still possible when approached in less sterile and more practical ways. This article shares teaching experiences that show just that outcome: when an equation is redesigned into a problemsolving story or a logic puzzle or is in some other way wrapped in meaning, even six-yearolds know enough mathematics to solve it.

Engaging Contexts for the Game of Nim

2007 ◽  
Vol 12 (5) ◽  
pp. 251-255
Author(s):  
Charles A. (andy) Reeves ◽  
Rosemarie Reeves Gleichowski
Keyword(s):  
Middle School ◽  
Problem Solving ◽  
Middle School Teachers ◽  
Algebraic Reasoning ◽  
School Teachers ◽  
Spatial Sense ◽  
Problem Solving Strategies

Middle school teachers realize the value of students playing games in mathematics classes if those games emphasize problem-solving strategies, algebraic reasoning, or spatial sense.

Research into Practice: Developing Algebraic Reasoning in the Elementary Grades

1998 ◽  
Vol 5 (4) ◽  
pp. 225-229
Author(s):  
Jinfa Cai
Keyword(s):  
Problem Solving ◽  
Algebraic Approach ◽  
Algebraic Reasoning ◽  
Elementary Grades ◽  
Problem Situations ◽  
Concrete Objects ◽  
Direct Modeling ◽  
Students First ◽  
Problem Solving Strategy ◽  
Solving Strategy

Direct modeling with concrete objects can be a powerful problem-solving strategy for young children (Chambers 1996). However, as problem situations become more complex. the value of more powerful strategies becomes apparent. An algebraic approach in which students first describe the problem using an unknow n in an equation and then solve for the unknown (Lesh, Post, and Behr 1987) is one such strategy.

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

2016 ◽  
Vol 29 (2) ◽  
pp. 129-150 ◽  
Author(s):  
Michalis Sialaros ◽  
Jean Christianidis
Keyword(s):  
Comparative Analysis ◽  
Problem Solving ◽  
Theorem Proving ◽  
Algebraic Reasoning ◽  
Numerical Problem ◽  
Controversial Topic ◽  
Methodological Approaches ◽  
Greek Mathematics ◽  
Geometrical Algebra

ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related toElem.II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

scholarly journals Profil Penalaran Aljabar Siswa SMA yang Memiliki Kecerdasan Linguistik dan Logis-Matematis dalam Memecahkan Masalah Matematika

MATHEdunesa ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 459-464
Author(s):  
Ulifah Istinaro ◽  
Rini Setianingsih
Keyword(s):  
High School Students ◽  
Problem Solving ◽  
Answer Sheet ◽  
Algebraic Reasoning ◽  
School Students ◽  
Algebra Students ◽  
Different Types ◽  
Mathematical Problems ◽  
The Subject ◽  
Academic Year

In learning algebra, students must have understanding about algebraic symbols and the meaning of equality and inequality, these abilities can be explored in algebraic reasoning which includes skills in finding patterns, recognizing patterns, and generalizing patterns. One way that teachers can carry out in order to develop students’ algebraic reasoning is through problem solving. Problem solving used to develop students’ algebraic reasoning is algebraic problem solving. Algebraic reasoning skills and problem solving for students are influenced by the intelligence possessed by students. Gardner identifies intelligence consisting of 8 intelligences, two of which are linguistic and logical-mathematical intelligence. This study attempt to describe the algebraic reasoning profile of high school students who have linguistic intelligence and logical-mathematical intelligence in solving mathematical problems. This research uses a qualitative approach. This research was conducted in class XI-1 of SMAN 7 Surabaya in the academic year 2018/2019. The subject of this study consisted of 2 students with different types of intelligence. The results showed that each student meets algebraic reasoning indicators. Student who have linguistic intelligence write answers completely but not detailed, but when explaining what is written on the answer sheet, the student explains in detail by using her own words. While student who have logical-mathematical intelligence write answers completely and in detail, but when the student explains what is written on the answer sheet, the student explains it in her own words but not in detail.

scholarly journals IDENTIFIKASI PENALARAN ALJABAR MAHASISWA DALAM MENYELESAIKAN MASALAH RELASI REKURSIF MENGGUNAKAN ALAT PERAGA MENARA HANOI DITINJAU DARI GAYA BELAJAR

2020 ◽  
Vol 14 (4) ◽  
pp. 565-574
Author(s):  
Nur Fitriyah Indraswari ◽  
Siti Zakiyah
Keyword(s):  
Problem Solving ◽  
Learning Styles ◽  
Learning Style ◽  
Data Interpretation ◽  
Algebraic Reasoning ◽  
Exploratory Research ◽  
Study Program ◽  
Level 3 ◽  
Level 2 ◽  
And Task

This study aims to identify the level of students' algebraic reasoning in solving recursive relation problems using tower hanoi props in terms of learning styles. This research is a descriptive exploratory research with a qualitative approach. The instruments in this study consisted of learning style questionnaires, Mathematics Ability Tests, Problem Solving Tasks, and task-based interviews. The research begins with giving tests of mathematical ability and learning style agket to 8 semester VI students of the STKIP PGRI Sumenep mathematics education study program in Sumenep to obtain three subjects, each with visual, auditory and kinesthetic learning styles with equal mathematical abilities and of the same gender. After that, it was followed by giving problem solving tasks and task-based interviews twice. Time triangulation is used to check the validity of the data. The data analysis technique consists of 5 stages, namely data categorization, data reduction, data presentation, data interpretation, and drawing conclusions. The results show that the visual subject is higher than level 2 but has not reached level 3, the auditory subject is at level 2, and the kinesthetic subject is at level 3. The three subjects have reached the stage of solving the problem, but the one who can solve the problem until they find the final solution is only the kinesthetic subject. The implication of research in learning is that teachers can more easily design learning according to their learning styles so that they can hone students' algebraic reasoning.

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