This study examined teachers' level of understanding of mathematical language and how it impacts student achievement in Nigeria. The study found:
1) Most teachers had insufficient understanding of mathematical terms, as shown by their inability to fully explain concepts and apply terms in daily examples.
2) Experience influenced understanding, with more experienced teachers showing a higher level of comprehension.
3) Over half of observed teachers had sufficient understanding to teach concepts, but 20% struggled with explanations of mathematical language.
4) The study suggests improving teacher training to enhance understanding of mathematical register in order to improve student learning outcomes.
Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
Enhancing Pupils’ Knowledge of Mathematical Concepts through Game and Poemiosrjce
The study investigated the effects of game and poem enhanced instruction on pupils’ knowledge of
mathematics concepts in mathematics (Fractions and decimals, Volume of, cylinder; triangular prisms and
sphere; Capacity and Weight). A total of 344 pupils from twelve (12) public primary schools of Ogbia and
Yenagoa Local Government Areas of Bayelsa State, Nigeria were involved in the study. A pretest-posttest
control group quasi-experimental design was adopted in the research. The moderating effects of gender were
also examined on the independent and dependent variables. Using ANCOVA statistics, the results revealed that
pupils exposed to game and poem enhanced instruction have better mean score in knowledge of mathematics
concepts than the control groups. Poem was found to be more effective in improving pupils’ knowledge of
mathematics concepts than game and a non-significant gender difference existed in the mean scores in
knowledge of mathematics concepts. There was no significant interaction effect of gender on pupils’ knowledge
of mathematics concepts. The implication of the findings was discussed and appropriate recommendations were
made.
Developing a Learning Trajectory on Fraction Topics by Using Realistic Mathem...iosrjce
This research and development was purposed at (1) developing a learning trajectory on fraction
topics by using Realistic Mathematics Education approach in Primary School; and (2) determining the validity,
practicality, and the effectiveness of the learning trajectory. The results of this research were (1) a learning
trajectory on fraction topics in the form of Teacher’s Guide Book and Student’s Book. (2) Teachers’ Guide Book
and the Student’s Book of learning trajectory were considered valid, practical and effective after being judged
by experts in Mathematics Educators, Language Educators, Experienced Teachers and an Educationalist.
Based on the research results, it can be concluded that the learning trajectory on Fraction Topics by using
Realistic Mathematics Education Approach can be effectively used to improve the learning effectiveness on
Fraction Topics in Primary School.
Enhancing Pupils’ Knowledge of Mathematical Concepts through Game and Poemiosrjce
The study investigated the effects of game and poem enhanced instruction on pupils’ knowledge of
mathematics concepts in mathematics (Fractions and decimals, Volume of, cylinder; triangular prisms and
sphere; Capacity and Weight). A total of 344 pupils from twelve (12) public primary schools of Ogbia and
Yenagoa Local Government Areas of Bayelsa State, Nigeria were involved in the study. A pretest-posttest
control group quasi-experimental design was adopted in the research. The moderating effects of gender were
also examined on the independent and dependent variables. Using ANCOVA statistics, the results revealed that
pupils exposed to game and poem enhanced instruction have better mean score in knowledge of mathematics
concepts than the control groups. Poem was found to be more effective in improving pupils’ knowledge of
mathematics concepts than game and a non-significant gender difference existed in the mean scores in
knowledge of mathematics concepts. There was no significant interaction effect of gender on pupils’ knowledge
of mathematics concepts. The implication of the findings was discussed and appropriate recommendations were
made.
A Research Proposal entitled “LEARNERS’ PREFERENCES AND TEACHING STRATEGIES IN TEACHING MATHEMATICS OF FOURTH YEAR HIGH SCHOOL STUDENTS AT MABITAC, LAGUNA S.Y. 2010-2011”
The aims of research consist of the following (1) to know need analyze teaching materials related to the matter on writing kid stories in the fourth grade of elementary school, (2) to develop teaching material on writing kid stories based on contextual. The study employs descriptive qualitative and evaluative method which the data are collected by interview, observation, document analysis, and Forum Group Discussions (FGD), questionnaire, and test. Result of the research (1) The teachers still need the addition of teaching materials on writing kid stories as support, (2) Teachers need the new innovation about the developing og teaching materials on writing kid stories. Teaching materials on writing kid stories on contextual basis which can help the teachers as the teaching media in enlanging the sight on writing kid stories and the students are motivated in expressing idea, opinion and mind in a story. The results of the development of teaching materials to writing kid stories based on contextual grade 4th can be received well by learners.
Summarizing 4 Journal Articles about English textbook evaluation Samialsadi1
Summarizing 4 Journal Articles about English textbook evaluation as required by our Dr Shanti under Syllabus and Materials Design Subject. Universiti Teknologi Malaysia (UTM)
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...AJHSSR Journal
This article is about an analysis of teachers’ Pedagogical Content Knowledge (PCK) during
teaching the concept of number for early childhood. Research subjects were three kindergarten teachers in
Depok area, West Java, Indonesia. This type of research is qualitative that analyzed the phenomenon of PCK
when teaching the concept of numbers to children aged 5-6 years. Researchers conducted two observations,
interviews and documentation studies. The results showed that the three respondents did not understand the
concept of numbers as a whole. Respondents also did not comprehend the definition of the concept of numbers
and the appropriate stages associated with the concept of numbers. In addition, the three teachers did not
understand the overall curriculum of early childhood education. However, with their sufficient teaching
experience, they were considered to have good teaching skills and good evaluation of learning process. The
obstacle faced by them was quite the same in which they still found it difficult to teach the concept of numbers
with different characteristics of children. It required a particular strategy for the teachers to overcome these
obstacles. The results of this study is expected to be a consideration to hold a professional workshop
development program in order to improve the professionalism of early childhood teachers particularly in
teaching mathematics.
A Research Proposal entitled “LEARNERS’ PREFERENCES AND TEACHING STRATEGIES IN TEACHING MATHEMATICS OF FOURTH YEAR HIGH SCHOOL STUDENTS AT MABITAC, LAGUNA S.Y. 2010-2011”
The aims of research consist of the following (1) to know need analyze teaching materials related to the matter on writing kid stories in the fourth grade of elementary school, (2) to develop teaching material on writing kid stories based on contextual. The study employs descriptive qualitative and evaluative method which the data are collected by interview, observation, document analysis, and Forum Group Discussions (FGD), questionnaire, and test. Result of the research (1) The teachers still need the addition of teaching materials on writing kid stories as support, (2) Teachers need the new innovation about the developing og teaching materials on writing kid stories. Teaching materials on writing kid stories on contextual basis which can help the teachers as the teaching media in enlanging the sight on writing kid stories and the students are motivated in expressing idea, opinion and mind in a story. The results of the development of teaching materials to writing kid stories based on contextual grade 4th can be received well by learners.
Summarizing 4 Journal Articles about English textbook evaluation Samialsadi1
Summarizing 4 Journal Articles about English textbook evaluation as required by our Dr Shanti under Syllabus and Materials Design Subject. Universiti Teknologi Malaysia (UTM)
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...AJHSSR Journal
This article is about an analysis of teachers’ Pedagogical Content Knowledge (PCK) during
teaching the concept of number for early childhood. Research subjects were three kindergarten teachers in
Depok area, West Java, Indonesia. This type of research is qualitative that analyzed the phenomenon of PCK
when teaching the concept of numbers to children aged 5-6 years. Researchers conducted two observations,
interviews and documentation studies. The results showed that the three respondents did not understand the
concept of numbers as a whole. Respondents also did not comprehend the definition of the concept of numbers
and the appropriate stages associated with the concept of numbers. In addition, the three teachers did not
understand the overall curriculum of early childhood education. However, with their sufficient teaching
experience, they were considered to have good teaching skills and good evaluation of learning process. The
obstacle faced by them was quite the same in which they still found it difficult to teach the concept of numbers
with different characteristics of children. It required a particular strategy for the teachers to overcome these
obstacles. The results of this study is expected to be a consideration to hold a professional workshop
development program in order to improve the professionalism of early childhood teachers particularly in
teaching mathematics.
READING COMPREHENSION AND PROBLEM SOLVING SKILLS OF GRADE SEVENSTUDENTS: A MI...AJHSSR Journal
ABSTRACT: The purpose of this study was to determine the relationship between the extent of students‟
reading comprehension and problem solving skills and identify teaching strategies that would address the
problem in teaching problem solving in Mathematics. The research utilized mixed explanatory design. The
subject consists of 189 grade 7 students who were part of the general section enrolled at Davao City National
High School. Purposive sampling was used in identifying the respondents taking the reading comprehension test
and problem solving test while random sampling was used in identifying participants for the key informant
interview. The result of the study revealed that students reading comprehension and problem solving skills were
at developing level. Moreover, reading comprehension skill was a predictor of problem solving skill. This
means that students‟ problem solving skill is dependent on their reading skills. Results also showed from the
conducted focus group discussion that students gave importance to vocabulary and main idea in learning
problem solving. Furthermore, using differentiated instruction was the identified best teaching strategy to
understand problem solving.
Maribel L. Alegarbes1
Master Teacher, Carcar Central National High School, Carcar City Division, Philippines
maribel.alegarbes@deped.gov.ph
Abstract: This research aimed to determine the teachers’ level of knowledge and attitude, stressors and coping
mechanisms in handling learners with learning difficulties at Carcar City Division, Carcar City, Cebu for the
school year 2019 - 2020. The twenty (20) respondents were selected using universal sampling technique. Survey
and interview questionnaires were utilized to obtain the desired results of the study. Weighted mean, percentage,
Chi – square Test of Independence, Pearson r and Colaizzi’s Method of Analysis were used in analyzing the data.
Findings revealed that the teachers are moderately knowledgeable in handling learners with learning difficulties
mainstreamed in an inclusive classroom setting. Moreover, teachers in Carcar City Division strongly support the
integration of learners with learning difficulties in an inclusive classroom setting as shown in their positive attitude
in handling these types of learners. Additionally, the teachers considered high extent of usefulness in utilizing
various cognitive, social, emotional, physical and spiritual coping mechanisms to combat stressors while handling
learners with learning difficulties. There is a positive significant correlation between teacher’s level of knowledge,
attitude and usage of coping mechanisms to their years of experience and highest educational attainment.
Knowledge is also positively correlated to their level of attitude and usage of coping mechanisms. The stressors
encountered by the teachers in handling learners with learning difficulties in an inclusive classroom are
administrative concerns and support, parental issues and behavioral issues of learners with learning difficulties
integrated with the regular students. Hence, the teachers of Carcar City Division handling learners with learning
difficulties have observed a range of stressors that could have a tremendous effect to the teaching effectiveness.
A Study on Interest in Mathematics Interest and its Relation to Academic Achi...ijtsrd
In our match towards scientific and technological advancement, we need nothing short of good performance in mathematics at all levels of schooling. In an effort to achieve this, this study investigated the impact of motivation on students' school academic achievement in mathematics in secondary schools using motivation measuring instrument and achievement test in mathematics. Six hypotheses were tested for significant at 0.05 margin of error using t test and analysis of variance ANOVA Results showed that gender difference and Parents Income were significant when impact of motivation on academic achievement was compared in male and female students. Also other result indicates significant difference when extent of motivation was taken as variable of interest on academic achievement in mathematics based on the degree of their motivation. Implications, suggestions and recommendations on students, parents, government, counsellors, educational stakeholders, etc were discussed. Ms. S. Kalpana | Ms. V. A. Malathi ""A Study on Interest in Mathematics Interest and its Relation to Academic Achievement in Mathematics Among Higher Secondary Students"" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-4 , June 2019, URL: https://www.ijtsrd.com/papers/ijtsrd25113.pdf
Paper URL: https://www.ijtsrd.com/humanities-and-the-arts/education/25113/a-study-on-interest-in-mathematics-interest-and-its-relation-to-academic-achievement-in-mathematics-among-higher-secondary-students/ms-s-kalpana
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
PHP Frameworks: I want to break free (IPC Berlin 2024)Ralf Eggert
In this presentation, we examine the challenges and limitations of relying too heavily on PHP frameworks in web development. We discuss the history of PHP and its frameworks to understand how this dependence has evolved. The focus will be on providing concrete tips and strategies to reduce reliance on these frameworks, based on real-world examples and practical considerations. The goal is to equip developers with the skills and knowledge to create more flexible and future-proof web applications. We'll explore the importance of maintaining autonomy in a rapidly changing tech landscape and how to make informed decisions in PHP development.
This talk is aimed at encouraging a more independent approach to using PHP frameworks, moving towards a more flexible and future-proof approach to PHP development.
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
GridMate - End to end testing is a critical piece to ensure quality and avoid...ThomasParaiso2
End to end testing is a critical piece to ensure quality and avoid regressions. In this session, we share our journey building an E2E testing pipeline for GridMate components (LWC and Aura) using Cypress, JSForce, FakerJS…
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
State of ICS and IoT Cyber Threat Landscape Report 2024 previewPrayukth K V
The IoT and OT threat landscape report has been prepared by the Threat Research Team at Sectrio using data from Sectrio, cyber threat intelligence farming facilities spread across over 85 cities around the world. In addition, Sectrio also runs AI-based advanced threat and payload engagement facilities that serve as sinks to attract and engage sophisticated threat actors, and newer malware including new variants and latent threats that are at an earlier stage of development.
The latest edition of the OT/ICS and IoT security Threat Landscape Report 2024 also covers:
State of global ICS asset and network exposure
Sectoral targets and attacks as well as the cost of ransom
Global APT activity, AI usage, actor and tactic profiles, and implications
Rise in volumes of AI-powered cyberattacks
Major cyber events in 2024
Malware and malicious payload trends
Cyberattack types and targets
Vulnerability exploit attempts on CVEs
Attacks on counties – USA
Expansion of bot farms – how, where, and why
In-depth analysis of the cyber threat landscape across North America, South America, Europe, APAC, and the Middle East
Why are attacks on smart factories rising?
Cyber risk predictions
Axis of attacks – Europe
Systemic attacks in the Middle East
Download the full report from here:
https://sectrio.com/resources/ot-threat-landscape-reports/sectrio-releases-ot-ics-and-iot-security-threat-landscape-report-2024/
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
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We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Generative AI Deep Dive: Advancing from Proof of Concept to ProductionAggregage
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Teachers’ level of understanding the language of mathematics as a determinant of students’ achievement in mathematics in nigeria
1. Journal of Education and Practice
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.4, No.22, 2013
www.iiste.org
Teachers’ Level of Understanding the Language of Mathematics
as a Determinant of Students’ Achievement in Mathematics in
Nigeria
Dr. Abiodun A. Popoola
Ekiti State University, Ado-Ekiti, Nigeria
E-mail: popabiodun2013@gmail.com
Abstract
The study examined the teachers’ level of understanding the language of Mathematics as a determinant of
students’ achievement in Mathematics in Nigeria. Participants included 50 teaching teachers and 1500 students
in Ekiti State, Nigeria, who answered questions on teachers’ level of understanding of Mathematical terms in the
daily use and applications, The data collected were analyzed descriptively using percentages, means and
standard deviations. Hypotheses were analyzed using chi-square and t- test. The outcome pointed out the
connection between teachers’ level of understanding and competencies displayed during lessons, relationship
between teachers’ level of understanding and students’ achievement in Mathematics among others. The study
shed light on the extent to which qualification, experience and sex have relationship on teachers cogent
interpretation and understanding of the Mathematical terms as determinant of students’ achievement in
Mathematics. It was suggested that secondary school teachers should learn to understand Mathematical language
in order to use it correctly in the classroom
Keyword: Register, Environment, Comprehend, Concept, Mathematics, Language
Introduction
Secondary school students seem to find Mathematics difficult to understand and apply Mathematics
language register when solving problems. The students seem to think that Mathematics is abstract. Some
Mathematics teachers seem to be deficient in the use of Mathematical language as a means of instruction. The
issue in this regard is the level of understanding of the language of Mathematics among the secondary school
teachers. Teachers who are good at the understanding of Mathematics register should be able to present everyday
problems in Mathematical form to students. This kind of exercise would certainly require a full understanding of
the concepts and terms of the subject. Teachers may be able to compute and arrive at correct answers when
solving problems posed to their students, but may create more problems as a result of their inabilities to fully
explain the technical terms and show their meaning in terms of daily use and application.
This problem is further exacerbated when the technical terms take on meanings that are different from
everyday use of the term. Therefore, this study investigated whether students will understand Mathematics better
if the terms are simplified within the socio- cultural environment of the students. The study further determined
the extent of understanding of the language of Mathematics by secondary school teachers in Nigeria. Teachers
were observed at work (classroom), interviewed and interacted with in order to determine the extent of their
understanding of Mathematics language
Literature Review
Many studies (Akpan, 1996; Franke, Carpenter, Fennema, Ansell, & Behrend, 1998 and An, Kulm &
Wu, 2004) have worked on the issue of competence of Mathematics teachers and their ability to explain
Mathematics fully. The opinion is that many teachers of Mathematics including prospective teachers in training
have little knowledge and understanding of school Mathematics than is required for the task they face in the
classroom. Others studies, Hiebart, Carpanter, Fenneman, Fuson, Wearne Murray (1997), Lin (2000), Geer
(2001), Hill & Ball (2004) and Burton, Daane & Giesen (2008) have also found similar thing that Mathematics
teachers in many countries have less than the required knowledge of the contents of Mathematics they teach.
This condition can probably be informed by the extent of the relevance and mastery of the contents of the
curriculum which these teachers were expose to during their training. If the Mathematics curricular in the
training departments were full of topics in school Mathematics, and these teachers were able to master the topics,
perhaps they would have displayed a better level of competency and preparation in the mastery of Mathematics
contents. It has however been shown by Ball & Brass (2000) Haylock (1982) and Simon & Blume (1994) that
the Mathematics contents of Mathematics education programme for undergraduates does not contain all that the
teachers of the subject at the secondary school need to acquire to qualify them to teach the subject at the
secondary school.
Mathematics teachers themselves probably are aware of their own deficiency in the mastery of
97
2. Journal of Education and Practice
ISSN 2222-1735 (Paper) ISSN 2222-288X (Online)
Vol.4, No.22, 2013
www.iiste.org
Mathematics contents (Shulman, (1986); Tamir, (1988); Eraut, (1994); Haylock & Cockburn, (2003); Ma, (1999)
and Lamb & Booker, (2003)). These teachers especially at the primary school level do not feel comfortable in
teaching Mathematics and this lack of self-confidence is as a result of lack of understanding of Mathematics
contents and also low level of Mathematics attainment while in school. A situation whereby Mathematics
teachers do not have enough knowledge of the subject matter and sense of incompetence is certainly a serious
problem to the teaching and learning of the subject in our schools. Studies, Wilcox, Lanier & Lappan (1992) &
Miller (1991) have shown that content courses that focus on content knowledge have been successful in making
the teachers to become competent and effective. Lack of understanding of the contents may serve as barriers to
how successful and competent teachers might handle the teaching-learning situations. One relevant question to
ask is that at what point do teachers begin to feel this sense of incompetence towards Mathematics teaching?
In measuring Mathematics contents proficiency regarding Mathematics teaching, Burton, Daane &
Giesen, 2008 reported that the content proficiency which Mathematics teachers are carrying to the teaching job
can be explained through teachers’ level of understanding and how fully they can explain the terms in the subject.
The study therefore looked into the relationship between teachers’ level of understanding of the cogent meaning
of Mathematical terms on students’ achievement in Mathematics.
Statement of the Problem
The low performance in Mathematics at the secondary school level has been of paramount concern to
educators, researchers and even the parents. It is possible that lack of teachers’ understanding of technical terms
in Mathematics is partly responsible for this low performance. In order to actually understand Mathematics idea
and concepts, the technical terms need to be well grasped. It seems as if some mathematics teachers do not have
adequate understanding of mathematics language and technical terms which seems to hinder students
understanding and achievement in mathematics. Observations by the researchers show that some mathematics
teachers were not able to fully explain the meaning of some concepts and found it difficult to discuss them
meaningfully so that students can understand better during the lessons. This study therefore investigated the
teachers’ level of understanding the concept of mathematics, technical terms as they affect the achievement of
students.
Purpose
The study examined teachers’ level of understanding the language of Mathematics as a determinant of
students’ achievement in Mathematics in Nigeria, also investigated the Mathematics language the teachers
understand in order to teach the students effectively in secondary school. The study also examined how the
teachers translate Mathematical language into cogent interpretations for students in the secondary schools
Questions
1.
2.
3.
Based on the problems of the study, the following research questions were raised to
guide the study:
Will experience of teacher influence the level of understanding the meaning used for teaching
Mathematics in school?
How well do teachers of Mathematics understand the meaning and able to explain the
Mathematical terms during class lesson?
DO teachers of Mathematics able to translate their understanding into cogent interpretation on the
daily use to students?
Hypotheses
1.
There is no significant difference between NCE teachers and other graduates in the understanding
of Mathematical terms
2.
There is no significant relationship between Students’ performance and teachers’ level of
understanding of Mathematical terms.
3.
There is no significant relationship between teachers’ teaching experience and cogent
understanding of Mathematical terms.
4.
There is no significant relationship between sex and cogent understanding of Mathematical terms
Methodology
Design:
A descriptive research design of the survey type was used in the study.
98
3. Journal of Education and Practice
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Population
Participants were secondary school teachers who had been teaching in the school in the last one year and
secondary school II (SSS2) students in 172 public schools in Ekiti State, Nigeria, numbering about seventeen
thousand (16,887) as at 2009/2010 academic session according to the Ekiti State Ministry of Education Records.
These teachers have taken some courses in their higher institutions of learning. These students are distributed all
over the sixteen (16) Local Government Areas of Ekiti State
Sample and Sampling Techniques: The sample consisted of 50 secondary school teachers teaching
Mathematics and about seventeen thousand (16,887) SSSII students as at 2009/2010 academic session
according to the Ekiti State Ministry of Education records were selected from 50 Secondary Schools in Nigeria
out of which 50 teachers and 1500 students responded to questionnaires on teachers’ abilities to fully explain the
technical terms and show their meaning in terms of daily use and application, while students responded to
whether they understand Mathematics better if the terms are simplified within the socio- cultural environment of
the students schools in six Local Government Areas (LGA) of Ekiti- State. The selection was based on
multistage sampling technique. Stage 1 was random selection of six LGAs, while stage 2 was random selection
of schools using purposive random sampling techniques. The schools were to satisfy the following criteria: 1.
They must be co-educational 2. Have been presenting candidates for Senior Secondary School Certificate
Examinations for at least five consecutive years and have at least two qualified mathematics teachers.
Instruments: Data were collected through ‘Mathematical In- class Questions for Mathematics Teachers (MIQT).
MIQT contains bio-data of the respondent’ school, local government area, sex, area of subject specialization,
teaching experience and qualification. The other section was ‘Mathematical In- class Questions’( an achievement
test) constructed by the researcher to measure teacher’s level of understanding(facilitating learning, using
content effectively, knowledge in teaching, addressing students’ difficulties in Mathematics, building on students’
Mathematical ideas, directing students’ Mathematical thinking, engaging students in Mathematical activities,
promoting students’ Mathematical thinking, ways in which teachers use to explain Mathematics to students,
what is expected of the students when they are required to explain some terms and how to evaluate students’
understanding during class lesson among others). The test was designed to provide response on 5-item scale
dimensions to be answered by the teachers, given a total of 30 marks. Teachers were also observed during class
lessons twice per week for 24 weeks to assess how the teachers can facilitate learning, using content effectively,
knowledge in teaching, addressing students’ difficulties in Mathematics, building on students’ Mathematical
ideas, directing students’ Mathematical thinking, engaging students in Mathematical activities, promoting
students’ Mathematical thinking, ways in which teachers use to explain Mathematics to students, what is
expected of the students when they are required to explain some terms and how to evaluate students’
understanding during class lesson. “Students’ In- class test on Mathematics (SIMT) is based on teachers’ level
of understanding of Mathematical Terms was administered on the students. The first part of SIMT contains biodata of the respondent’s school, class, sex and local government area, while, the second part contains students
attempting to provide answers to a 12- items question on terms used by teachers in their best abilities in order to
build on their Mathematical knowledge, ideas, in promoting students’ thinking, directing, engaging students in
Mathematical activities, and addressing students’ difficulties among others. The items are specifically designed
to provide correct conceptions on clearly defined content areas. Each of the items was marked based on the
responses provided. The contents were items used in the classroom that can determine their level of
understanding. Below are some examples of the question used in the instrument for the students:
a. What would you do when you are to: factorize, expand, simplify some identified problems in Mathematics?
b. Arrange in order of magnitude: 5/9, 7/15, 11/20, 3/8
c. Simplify: x-5ax+ 3x - 7ax -2
The authors developed the items and three experts in Curriculum Studies Department and Tests and
Measurement Department respectively, and two secondary school teachers and tertiary educators did the content
validation for relevance and accuracy. The instruments were used for a pilot study of fifteen teachers of
mathematics and one hundred senior secondary school students. The instrument was first administered and
observation taken while a retest was carried out after three weeks and scores were collected. The scores for the
two instruments MIQT and SIMT where collated and subjected to Pearson’s Product Moment Correlation
statistics. The result yielded correlation co efficient of 0.79 and 0.86 respectively which were considered to be
statistically good enough for the instrument to be used for this study personally administered to the respondents.
Data Analysis: The research questions were pre-coded and analyzed using descriptive statistics: frequency
counts and percentages. A correct response in the sub- questions was scored 1 if the respondent gave the correct
answer and scored 0 if the respondent gave the wrong answer or response. All the points were added to give a
total score ranging between 0 and 30 for both teachers and students. Hypotheses were tested using Means,
Standard Deviations, chi-square tests and pie charts. All hypotheses generated were tested at α- level of 0.05.
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Results
Descriptive Analysis
The research questions were analysed using descriptive statistics and results were reported thus:
1. Will experience of teacher influence the level of understanding the meaning used for teaching Mathematics in
school?
Table 1 shows the difference in the Means(15.71) and standard deviations(12.49) of the teachers’ experience in
content explanation, promote students thinking, directing, engaging students in Mathematical activities, and
addressing students difficulties which was used to categorized the teachers into insufficient and sufficient.
Hence, any teacher whose mean and standard deviation falls in (0 - 3.22) was classified as having insufficient
understanding in Mathematics. Those whose mean and standard deviation fall in (3.23- 18.20) was classified as
having sufficient understanding in Mathematics, while, the teacher whose mean and standard deviation fall in
(18.18 -21.00) was classified as having high understanding in Mathematical language/ terms. Year of experience
1 -5 of teachers are 32 (64%) have insufficient understanding of Mathematical language/ terms, and between
years 6 and 10 5(10%) of the teachers have sufficient understanding of Mathematical language/ terms, while
13(26%) of teachers who have their experience above 10 years have a high understanding of Mathematical
language/ terms. Hence, 18 out of 50 teachers have sufficient understanding of Mathematical language/ terms
while,32 teachers out of 50 have insufficient understanding of Mathematical language/ terms.
Table 1
Teachers’ experience on the level of understanding in Mathematical language/ terms
Experience difference in year among the Range
of
Mean
and Frequency
Percentage
teachers
Standard Deviation
1-5
0- 3.22
32
64%
6-10
3.23-18.19
5
10%
Above 10
18.20-21.00
13
26%
Total
50
100%
2. How well do teachers of Mathematics understand the meaning and able to explain the
Mathematical terms during class lesson?
Teachers were observation during class lesson and the following were used:
i.
Mathematical knowledge(content)
ii.
Building on students’ Mathematical ideas, iii. Promoting students’ thinking,
iv.
Engaging students in Mathematical activities,
v.
Addressing students’ difficulties.
vi.
Ability to explain sufficiently
vii.
Content knowledge of the subject
viii.
Skillfulness of the teacher to manage the students during Mathematics lesson
ix.
Ability to show sufficient understanding
The results of the observation during teaching are as follows:
Table2
Analysis of teachers’ level of understanding and explanations of mathematical terms during Mathematics
lesson
Level of teachers Understanding
Range
Frequency
Percentage
Insufficient understanding
0-39
10
20
Sufficient understanding
40-59
28
56
High understanding
60- above
12
24
Total
50
100
Table 2, figure 1 shows that, out of 50 teachers who were observed, only 10(20%) scored in the range of 0- 39
are categorized as insufficient understanding of the meaning of Mathematical terms. This is followed by 28(56%)
of teachers with the range between 40- 59 are categorized as those with sufficient understanding of the meaning
of Mathematical terms. While, only 12(24%) whose scores are between the range of 60 and above are
categorized as having high understanding of the meaning of Mathematical terms. Hence, 28(56%) of teachers
whose scores are between 40- 59 are categorized as having the highest record of sufficient understanding of the
meaning of Mathematics concepts and terminology.
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Insufficient understanding
High understanding
Sufficient understanding
Figure 1: Teachers’ level of understanding of Mathematical terms
3. Do teachers of Mathematics able to translate their understanding into cogent interpretation on the daily use
to students?
Table3
Translation of teachers understanding into cogent interpretation on the daily use to students.
Frequency
Percentage
cogent interpretation
Insufficient
10
20
Sufficient
34
68
High sufficient
6
12
Total
50
100
Table 3, figure 2 show that, out of 50 teachers examined, 10(20%) could not sufficiently translate their
understanding into cogent interpretations of mathematical terms for the daily use in the classrooms to enhance
student understanding. Thirty-four (68%) of the teachers could sufficiently translate their understanding into
cogent interpretations for proper teaching of students, while, only 6(12%) had high translation of Mathematical
terms into cogent interpretation for the teaching of students. Hence, those teachers who could translate their
understanding Mathematics into cogent interpretations for proper teaching of students are more than the other.
High understanding
Insufficient understanding
Sufficient understanding
Figure 2: Teachers’ ability to translate understanding to cogent interpretation for the daily application by
students
Hypotheses Testing
1.
There is no significant difference between NCE and other graduates in the understanding of
Mathematical terms .This can be analyzed descriptively
Table 4
Teacher’s Qualification in terms of their level of understanding of Mathematical language/ terms
Frequency
Percentage
Qualification of teachers
NCE
23
46%
BSc/BA/BSc (Ed)/BA(Ed)
23
46%
M.Ed/ Ph.D
4
8%
Total
50
100
Table 4 shows the qualification of teachers according to their level of understanding of Mathematical
terms. Only 23 (46%) of NCE graduates have the understanding of
Mathematical language / terms while, 23
(46%) of the B.Sc/BA/B.Sc (Ed)/BA(Ed) teachers have the understanding of Mathematical language/ terms.
Only 4(8%) of teachers have M.Ed/ Ph.D with their understanding of Mathematical language/ terms. Hence,
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teachers who are NCE and BSc/BA/BSc (Ed)/BA(Ed) have sufficient understanding of Mathematical language/
terms. This is also analysed using t - test statistics as shown below:
Table 5
Mathematical teacher’s qualification and level of understanding of Mathematical terms
Qualification
N
Mean
SD
Mean diff.
df
t- cal
t-tab
NCE
23
17.13
17.61
2.63
48
0.732 2.00
Other
27
14.50
5.80
p> 0.05
Table 5 shows the difference in teachers’ qualification and understanding of Mathematical terms. NCE
graduates had a mean score of 17.13 with the standard deviation of 17.61, compared to Mathematical teachers
who had other qualifications with a mean score of 14.50 and a standard deviation of 5.80. The t- calculated was
found to be 0.732, while, t-table was found to be 2.00 at α - level of 0.05. Hence, the null hypothesis was not
rejected. Therefore, there is a no significant difference in the level of understanding of Mathematical term
among the NCE and other graduates.
2. There is no significant relationship between Students’ performance and teachers level of understanding of
Mathematical terms.
Table 6
Pearson correlation of Students performance and teachers level of understanding of Mathematical terms.
Variable
N
Mean
SD
r-cal
r-tab
Student performance
1500
12.61
11.16
0.714
0.273
Teachers level of understanding
50
15.71
12.49
Table 6 shows students’ performance and teachers’ level of understanding of Mathematical terms.
Students had a mean score of 12.61 with the standard deviation of 11.16 as compared to teachers’ level of
understanding of Mathematical language/ terms with a mean score of 15.71 and a standard deviation of 12.49.
The r- calculated was found to be 0.714 greater than r-table (0.273) at α -level of 0.05. Hence, the hypothesis is
rejected. Therefore, there is a significant difference between the students’ performance and teachers’ level of
understanding of Mathematical language/ terms
3. There is no significant relationship between teachers’ teaching experience and cogent understanding of
Mathematical terms.
Table 7
Chi-Square (x2) analysis of teaching experience and cogent understanding of Mathematical terms
Level of cogent understanding
1-5
6-10
Above 10 Total
df
X2cal
Table
Insufficient
6
23
3
32
(6)
(23)
(4)
4
0.859
9.49
Sufficient
1
3
1
5
(1)
(3)
(1)
Highly sufficient
3
8
2
13
(3)
(9)
(2)
Total
10
34
6
50
P<0.05
Table 7 shows that X2cal (0.859) is less than X2 table (9.49) at 0.05 level of significant. The hypothesis
is not rejected. This implies there is no significant relationship between teaching experience of teachers and
cogent understanding of Mathematical terms.
4. There is no significant relationship between sex and cogent understanding of Mathematical terms
Table 8
Chi-Square (x2) analysis of sex and teachers’ cogent understanding of Mathematical terms
Teachers’ level of
understanding Male
Female
Total
df
X2cal
X2table
according to sex
Insufficient
10
10
(3)
(7)
2
8.189
Sufficient
12
22
34
(11)
(23)
5.99
Highly sufficient
4
2
6
(2)
(4)
Total
16
34
50
P<0.05
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Table 8 shows the analysis of the sex and teachers’ cogent understanding of Mathematical terms. The
X2cal (8.189) is greater than X2table (5.99) at 0.05 level of significant. Therefore, the null hypothesis is rejected.
It implies that there is significant relationship between the sex difference of teachers and cogent understanding of
Mathematical terms.
Discussion
The analysis of the data shows that the experience of the teachers has influence on their understanding of
Mathematical language. From the analysis of the research question 1, only 26% of the teachers were classified as
having high understanding of Mathematical language and they were teachers who had taught for ten years and
above. While, those who had been teaching for between 6- 10years were 10%.
On their level of understanding and ability to explain Mathematics term during the lesson 56% of respondents
have sufficient understanding (at average level) while, 24% were above average.
The teachers who had ability to translate their understanding to cogent interpretation for the daily use of students
were 68% they had sufficient understanding on the average, while, 12% were above average.
The descriptive analyses of research questions 1 to 3 show that a relatively high percentage of the teachers were
on the average in terms of understanding language of Mathematics, Mathematical term and translating their
understanding to cogent interpretation that will enhance students ability to use Mathematics knowledge to solve
problems daily.
The finding from hypothesis one shows that qualification is not a significant factor in the teachers’
understanding of Mathematical terms. The implication could be that some NCE teachers are good at
Mathematical terms having improved their knowledge through private study while graduate teachers were
relying on their degrees. The findings corroborate the work of Burton, Daane& Giesen, 2008 that the content
proficiency which Mathematics teachers are carrying to the teaching job can only be explained through teachers’
level of understanding. On the findings from the analysis which tested relationship between students and
teachers understanding of Mathematics terms show that there is difference between the two variables. This
implies that teachers’ level of understanding will definitely influence students’ achievement. Hence, teachers’
contents knowledge and cogent interpretation of the content determined students’ achievement in Mathematics.
These findings corroborate the work of Ma, (1999) & Eraut, (19994) that Mathematics teachers need to have
enough knowledge for the cogent interpretation and translation of curriculum contents so that students can be
successful and teachers can handle teaching/ learning situation. The findings from the testing of relationship
between teaching experience and teachers’ ability to translate teaching experience to cogent understanding that
will enable students to use mathematical terms successfully show that there is no relationship between the two
variables. The implication is that teacher’ inability to translate their understandings to cogent understands for
student use may be as a result of not able to have enough knowledge of the subject matter and a sense of
competence while in school or that their teacher were not able to interpret the content to practical form. The
implication is that if these teachers were able to master the topics, perhaps they would have displayed a better
level of competency and preparation in mastery of Mathematics contents. The findings from the testing of
relationship between the sex of teachers and understanding of Mathematics language indicated that there is a
relationship between the two variables. This finding corroborate the work of Leder (1992) that gender
differences was found and the possible explanations for the existing differences include teacher’s inability to
explain the content properly to learners’ related variables as well as cognitive variables.
Conclusion / Recommendations
Findings of this study further established that less than half of the teachers have sufficient understanding of
Mathematical language terms. More than half of the teachers who were observed during lessons had high
understanding of the meaning of mathematical terms. Also, more teachers were found able to interpret into
cogent understanding of Mathematical language. NCE and BSc/BA/BSc (Ed)/BA(Ed) have sufficient
understanding of Mathematical language/ terms. It was found that sex of teachers would not have a relationship
with the cogent interpretation of Mathematical language/ terms teaching. It is believed that teachers’
understanding of contents/ terms in order to make learning meaningful is paramount and have some implications
to Mathematics educators and policy makers in re- designing the course contents of the teachers education
programs in Nigeria. Teachers’ understanding of contents is important. Mathematical language and skills make
the greatest influence on the learning outcomes and attitude of the students. Teachers need to be skillful in order
to make learners achieve. He also needs to understand how to explain concepts and impact it on students in order
to ensure efficient and effective outcomes in Mathematics.
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Acknoledgements:
Prof. Afolabi Popoola, Faculty of Education, University of Ado-Ekiti, Nigeria
popefolabi@gmail.com
Prof. Olu G Oyinloye, Faculty of Education, University of Ado-Ekiti, Nigeria
Email: olugaby33@ yahoo.com
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