Problem Posing and Solving: Strategic Italian Key Action to Enhance Teaching and Learning Mathematics and Informatics in the High School

Author(s):  
Anna Brancaccio ◽  
Marina Marchisio ◽  
Carmela Palumbo ◽  
Claudio Pardini ◽  
Amelio Patrucco ◽  
...  
2019 ◽  
Vol 112 (6) ◽  
pp. 404

Working to correct misconceptions and errors is a natural part of teaching and learning mathematics. Rather than seeing errors as something to avoid, how can teachers and students capitalize on them to create learning opportunities? Catalyzing Change in High School Mathematics: Initiating Critical Conversations suggests that teachers actively plan for student errors and misconceptions by designing lessons that— promote a classroom culture in which mistakes and errors are viewed as important reasoning opportunities to encourage a wider range of students to engage in mathematical discussions with their peers and the teacher. (NCTM 2018, p. 34)


2019 ◽  
Vol 6 (2) ◽  
pp. 222-232
Author(s):  
Fransiskus Magnis Pastoriko ◽  
Kana Hidayati ◽  
Rasmuin Rasmuin

Homework had become a tradition in teaching and learning mathematics in school. Even so, in Indonesia, there is not enough research on homework. Our research is conducted to investigate high school students’ views on homework and to provide the basis for further research on homework in Indonesia. In this research, we use exploratory-descriptive qualitative to explore and describe the students’ view of homework. We collected the data from 124 high school students by using the structured interview conducted via online form. The data were analyzed by using the thematic analysis. Based on our results, we found that (1) students know that mathematics homework can help them with their academic achievement and their attitudes toward their studies, (2) mathematics homework is not high on their priority, (3) it makes them tired physically and mentally, and (4) students argue that mathematics problems are better to be solved in the class where they can ask the teacher. We also found their difficulties in doing their homework, such as (1) lack of knowledge (2) their teachers do not give them the necessary ‘tools’ to solve the problems, (3) they can’t ask for helping hands if they can’t solve the problems (4) some emotional  problems such as motivation, and (5) other priorities are higher on their list.


Author(s):  
Francesco Floris ◽  
Alice Barana ◽  
Anna Brancaccio ◽  
Alberto Conte ◽  
Cecilia Fissore ◽  
...  

In an Italian and European context, one of the fundamental skills in Mathematics is the ability to solve problems in everyday situations, often linked to everyday life. For this reason, the problem posing and solving methodology plays a fundamental role in the process of teaching and learning Mathematics. This paper presents the results of the immersive experience "Mathematical Exploration with Problem Posing and Solving", included in the teacher training activities proposed by the national PP&S - Problem Posing & Solving - Project of the Italian Ministry of Education, which aims at enhancing the teaching and learning of Mathematics by using new methodologies and technologies. In particular, the focus will be on the work and considerations of the 50 teachers who took part in the project, from both primary and secondary school. They were guided through the individual step-by-step creation of a contextualized problem, following a process guided through stimulus-based questions. This immersive experience brought about the production of valid problems and was full of very  stimulating teachers' considerations on the various phases of the problem posing and solving.


2020 ◽  
Vol 10 (1) ◽  
pp. 27-40
Author(s):  
Marvelino Manipol Niem ◽  
Rizza Untalan Veriña Veriña Veriñ ◽  
Emil Castillo Alcantara

The study was undertaken to determine the extent of integration of Information and Communication Technology (ICT) to Mathematics teaching and learning processes among Junior and Senior High School teachers in the Division of Tanauan City. Further, the research also identified various challenges encountered in ICT-based teaching and learning Mathematics. This study used mixed method of research to obtain the necessary data in the conduct of this research. Specifically, the researchers used survey questionnaire, interview, and focus group discussion with the 77 junior and senior high school Mathematics teachers from the division of Tanauan City. The actual number of respondents was determined using Raosoft sample size determination at five percent margin of error and used stratified random sampling. The Weighted Mean, Frequency Distribution, Percentage, Mean, Standard Deviation, and T-test were the statistical tools used to analyze the data gathered. Based on the findings of the study, majority of the respondents were female, bachelor’s graduate, from teachers I to III, 15 years below in the service and not active in the ICT – related seminars attended. Most of the respondents use technology in writing lesson plans, in computing students’ results and, in teaching the lesson through power point presentations. However, due to the lack of resources and little fund from the MOOE, the respondents rarely use telecommunication devices such as cable, satellite, fax-machine etc. to interact with pupils. There is a significant difference between the extent of the use of ICT in teaching and learning Mathematics and years in teaching. Different challenges like lack of ICT facilities, confidence in the use of ICT and lack of trainings attended were the most commonly identified by the respondents. With the aforementioned, the researchers recommended that Mathematics teachers must be given more opportunities to participate ICT-based seminars and trainings.


Author(s):  
Daria Rovan ◽  
Dubravka Glasnović Gracin ◽  
Goran Trupčević

In Croatia, as in many other countries, primary education teachers are trained as generalists and mathematics is only one of several different subjects that they teach, so when choosing their profession they are not necessarily drawn by their interest in becoming a mathematics teacher. Still, it is very important that they have a positive attitude towards mathematics and are motivated to teach it to their students. The aim of this study was to explore whether pre-service teachers with different achievement goal profiles have different beliefs about mathematics and teaching and learning mathematics. The participants were 325 pre-service primary education students. The research was conducted in three waves, during the students’ first, third and fifth year of study. In their first year of studies, we collected data on the achievement goals in mathematics that they had in high school, and self-efficacy in mathematics. Epistemic beliefs, subjective value of mathematics and mathematics anxiety were assessed at all measurement points. In their third and fifth year of study, we also collected data on the participants’ mathematics teaching efficacy beliefs and, in their fifth year, beliefs on teaching and learning mathematics. The results of the cluster analysis showed that we could group pre-service primary education teachers into three groups according to the profiles of their achievement goals in high school: (1) all goals high, (2) all goals low, (3) mastery orientation. The results showed differences between the groups in terms of motivation for learning mathematics at the beginning of their studies. However, these differences tend to be less prominent over time. At the end of their studies, they do not differ in their mathematics teaching efficacy beliefs or their beliefs about teaching and learning mathematics.Key words: achievement goals; mathematics education; motivation; teacher education; teachers’ beliefs---U Hrvatskoj, kao i u mnogim drugim zemljama, osnovnoškolski učitelji korisnici su generaliziranoga obrazovanja i Matematika je samo jedan od nekoliko različitih predmeta koje poučavaju, tako da ih pri odabiru profesije nužno ne privlači interes da budu učitelji matematike. Ipak, njihov pozitivan stav prema matematici i motivacija za poučavanje učenika matematici vrlo su važni. Cilj je ovoga istraživanja ispitati imaju li učitelji s različitim profilima ciljeva postignuća različita uvjerenja o matematici i poučavanju i učenju matematike. U istraživanju je sudjelovalo 325 studenata, budućih učitelja primarnoga obrazovanja. Istraživanje je provedeno u tri ciklusa: tijekom prve, treće i pete godine studija ispitanika. Na prvoj godini studija prikupljali smo podatke o ciljevima postignuća u matematici koje su sudionici imali u srednjoj školi i o samo-učinkovitosti u matematici. Epistemološka uvjerenja, subjektivnu vrijednost matematike i tjeskobu procjenjivali smo u svim ciklusima mjerenja. Na trećoj i petoj godini studija sudionika također smo prikupljali podatke o njihovim uvjerenjima o učinkovitosti u poučavanju matematike i, na petoj godini, uvjerenja o poučavanju i učenju matematike. Rezultati klaster analize pokazali su da se budući učitelji, studenti primarnoga obrazovanja, mogu grupirati u tri skupine prema profilima ciljeva postignuća u srednjoj školi: (1) svi visoki ciljevi, (2) svi niski ciljevi i (3) orijentacija prema vještini. Dobiveni rezultati pokazali su razlike između skupina s obzirom na motivaciju za učenje matematike na početku studija. Ipak, te su razlike manje uočljive tijekom vremena. Na kraju studija sudionici se ne razlikuju u svojim uvjerenjima o učinkovitosti u poučavanju matematike niti u svojim uvjerenjima o učenju matematike.Ključne riječi: ciljevi postignuća; matematičko obrazovanje; motivacija; obrazovanje učitelja; uvjerenja učitelja


Author(s):  
Yeping Li ◽  
Alan H. Schoenfeld

AbstractMathematics is fundamental for many professions, especially science, technology, and engineering. Yet, mathematics is often perceived as difficult and many students leave disciplines in science, technology, engineering, and mathematics (STEM) as a result, closing doors to scientific, engineering, and technological careers. In this editorial, we argue that how mathematics is traditionally viewed as “given” or “fixed” for students’ expected acquisition alienates many students and needs to be problematized. We propose an alternative approach to changes in mathematics education and show how the alternative also applies to STEM education.


1987 ◽  
Vol 71 (458) ◽  
pp. 314
Author(s):  
Paul Ernest ◽  
Peter G. Dean

SAGE Open ◽  
2016 ◽  
Vol 6 (4) ◽  
pp. 215824401667137 ◽  
Author(s):  
Judah Paul Makonye ◽  
Josiah Fakude

The study focused on the errors and misconceptions that learners manifest in the addition and subtraction of directed numbers. Skemp’s notions of relational and instrumental understanding of mathematics and Sfard’s participation and acquisition metaphors of learning mathematics informed the study. Data were collected from 35 Grade 8 learners’ exercise book responses to directed numbers tasks as well as through interviews. Content analysis was based on Kilpatrick et al.’s strands of mathematical proficiency. The findings were as follows: 83.3% of learners have misconceptions, 16.7% have procedural errors, 67% have strategic errors, and 28.6% have logical errors on addition and subtraction of directed numbers. The sources of the errors seemed to be lack of reference to mediating artifacts such as number lines or other real contextual situations when learning to deal with directed numbers. Learners seemed obsessed with positive numbers and addition operation frames—the first number ideas they encountered in school. They could not easily accommodate negative numbers or the subtraction operation involving negative integers. Another stumbling block seemed to be poor proficiency in English, which is the language of teaching and learning mathematics. The study recommends that building conceptual understanding on directed numbers and operations on them must be encouraged through use of multirepresentations and other contexts meaningful to learners. For that reason, we urge delayed use of calculators.


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