Arithmetic sequence paper

Mathematics Education Research Group of Australasia, 2014

Guided by the principles of lesson study as applied to microteaching, this paper discusses the results and conclusions of a series of activities done by some graduate students of De La Salle University, Philippines, in an attempt to test the applicability of the lesson – Sequence and Patterns – to facilitate the transition of seventh graders from arithmetic to algebra. The post-lesson discussion and a posteriori analysis proved the lesson to be a practical means to address the issue as it was able to put forward discourses and elaborations on possible students’ understanding of variables generated through attempts to describe patterns occurring in sequences presented. Algebra is an important area of mathematics used in generalising arithmetic through letters, symbols and signs—the use of which makes it an abstract subject (Ali Samo, 2009). Furthermore, the abstractness of algebra is one reason for students’ problems (Lee & Wheeler, 1989). It has been the practice of mathematics educ...

2020

This research aims to design an algebra learning sequence on the topic of linear equations in one variable-which was taught in Junior High School. We used design research method to do this, and preliminary design phase in particular. First, we designed a sequence of daily life problems in order for students can be familiar with this. This sequence of problems was used for designing a learning sequence. Next, we designed a sequence of learning according to the theory of Realistic Mathematics Education as this theory provides meaningful mathematics for students. Finally, we discussed the design to obtain final learning sequence for a teaching experiment. We consider that the result of the learning design is better than the conventional learning sequence, and it is more meaningful for students.

Proceedings of the annual meeting of the Georgia Association of Mathematics Teacher Educators, 2014

Many teachers have trouble transitioning their students between natural recursive thinking about the data and algebraic notation for representing linear functions (Zazkis & Liljedahl, 2002). In this study, we interviewed eighteen middle school students to see how they used prior instruction to think about a geometric pattern and construct its corresponding linear equation. All students were given the same task to complete and were questioned about their thinking during the interview. We found that the recording of pattern recognition plays a substantial part in helping students recognize and write explicit patterns. By having students decompose the total perimeter into how they saw the pattern growing, students were more successful in making the connection to the numeric representation of growth. In addition, they were better able to explain how they set up the equation, and the connection of each part of the equation to the original pattern. As teachers work with their students in developing a conceptual understanding of linear equations, it is critical that students are exposed to geometric patterns. The results of this study will help mathematics teacher educators better prepare teachers to develop their students' develop rich and connected mathematical understanding.

East Asian Journal of Multidisciplinary Research (EAJMR), 2024

This study looks into how future math teachers solve problems when dealing with sequences. Data show a worrying trend: none of the respondents received a very high score, and more than 60% received a low grade. The biggest obstacle turned out to be harmonic sequences, indicating a critical knowledge gap. Even simple sequences, such as arithmetic sequences, could be challenging, especially when phrased issues and non-consecutive phrases were included. It's interesting to note that students started using online tools like YouTube lessons as part of a self-help movement. This, however, draws attention to a possible over-reliance on outside sources. The study highlights how crucial it is to reinforce fundamental information across a range of sequence types. Future math teachers can approach and solve sequence issues with more confidence if they have a solid grasp of the fundamentals and have conducted purposeful web research. This will ultimately result in moreeffective teaching methods.

The aim of this paper is to describe the evolution of a teaching learning sequence for grade 6 students beginning algebra learning over a period of two years that included multiple trials. The teaching learning sequence was designed to enable the students to make a transition to algebra from arithmetic by connecting their prior knowledge of arithmetic and operations and exploiting the structure of arithmetic expressions. In the process, the study aimed to identify the concepts, rules and procedures which facilitate the connection between arithmetic and algebra and enable the transition. The repeated trials allowed us to see the potential of the two concepts 'term' and 'equality' identified during the study and the nature of tasks that help in making the connection between the two domains.

International Journal of Innovative Research and Development, 2020

Background to the Study Development in almost all areas of life is based on the knowledge of Mathematics. As a country, there cannot be meaningful development in virtually any area of life without the human resource base having vast knowledge in the concept of Mathematics. It is for this reason that the education system of countries that are concerned about their development put great deal of emphasis on the study of Mathematics. Mathematics is one of the essential subjects which are needed in everyday life. It is one of the prerequisite subjects needed by man in many subject areas. Meanwhile, many people on the other hand find it difficult to cope with it. This is due to the fact that most teachers who handle the subject do not use the right technique in teaching the subject. This situation scares most pupils and do not want to hear the name 'Mathematics'. Most teachers also haphazardly teach the subject since they themselves do not have the requisite skills. Also, more knowledgeable teachers sometimes overestimate the accessibility of symbols-bases representations and procedures (Nathan &Kiesinger, 2000). Most of the pupils perceive Mathematics to be a difficult subject which seems to be a misconception. Mathematics is not a difficult subject at all but the ability to solve Mathematics problems sometimes depend on the background of pupils and the way they view education. The numerous benefits of studying Linear Equations include: it could be applied in the fields of Engineering, Accountancy, Medicine and other equally important avenues like Marketing. It is also used in everyday life and helps in Logical Reasoning. Linear Equations involving one or more variables are one of the many topics in Mathematics that has gotten a wide area of applications. In this research, the researcher too looked at simple Linear Equations in one variable. That means there will be no terms, no 's just x terms and numbers. For example, we will see how to solve the equation 3 + 15 = + 25 using the Flag Diagram, the Least Common Multiple (LCM) method and the Balancing Method. The important thing to remember about Linear Equations is that, the 'equal sign' represents a 'balance'. What an 'equal sign' says is that, 'what is on the left-hand side is exactly the same as what is on the right-hand side'. In any Linear Equation, there is an unknown quantity say x, which is what we try to find. Linear Equations in one variable occurs so frequently in the solution of other problems like Word Problem (Story Problems) where the whole story is reduced to a Linear Equation to make the solving very simple. Thus, a thorough understanding of Linear Equations in one variable is very essential in the world of Mathematics.

for the learning of mathematics, 2015

For the Learning of Mathematics 35, 2 (July, 2015) FLM Publishing Association, Fredericton, New Brunswick, Canada Theoretical developments in mathematics education offer ways to understand disjunctures between school mathematics and the discipline of mathematics as a function of institutional schooling. For example, Chevallard (1989) offers the theoretical idea of didactical transposition for this purpose:

Pythagoras, 2019

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their solutions to linear equations in interviews. The article stems from a study that describes whether learners use mathematically endorsable narratives to explain and justify their solutions. Sfard’s theory of commognition is used to develop a framework for analysis of their discourse. The findings show that all learners use ritualised rather than explorative discourse, characterised by applying strict rules to operations with disobjectified entities. The only mathematical objects they produce endorsed narratives about are positive integers. Thus they do not meet the relevant curriculum requirements. Nevertheless, the analytic tools – adapted from Sfard specifically for the study of linear equations – give a particularly nuanced account of differences in the learners’ ritualised discourse. For example, some learners used endorsed narratives about negative integers, algebraic terms and the structure of an equation when prompted by the interviewer. There is not sufficient evidence to suggest that any learners are in transition to explorative discourse. However, the article shows that learner discourse is a rich resource for teachers to understand the extent to which learners are thinking exploratively, and offers suggestions for how their thinking can be shifted. This is an opportunity for teacher professional development and further research.

Pythagoras

Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations.This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their solutions to linear equations in interviews. The article stems from a study that describes whether learners use mathematically endorsable narratives to explain and justify their solutions. Sfard’s theory of commognition is used to develop a framework for analysis of their discourse.The findings show that all learners use ritualised rather than explorative discourse, characterised by applying strict rules to operations with disobjectified entities. The only mathematical objects they produce endorsed narratives about are positive integers. Thus they do not meet the relevant curriculum requirements. Nevertheless, the analytic tools – adapted from...

2012

To test a model which characterizes what is at stake in the situation of solving linear equations , we analyse talk of teachers who, stimulated by watching an animation of classroom interaction (Chazan & Herbst, in press) share with their colleagues how they teach their students how to solve linear equations. The teacher talk illustrates two key aspects of our model of the situation of solving linear equations. First, the teachers in the sample conceive of it as their responsibility to teach their students a method for solving this class of problems; applying the steps of the method successfully means knowing how to solve linear equations. Second, teaching the method of solving linear equations does not involve the presentation of mathematical arguments, but at the same time is not exactly justification-free; the teachers present students with similes that motivate the steps in the method.