Clinical-medicine education definition. Typically, PBL definitions for K–8 **mathematics** and science education that are inspired by clinical-medicine education situate PBL in the “learning by doing” principle of Dewey (1938). An illustrative definition of PBL following this tradition char- acterizes problem-based learning as “a teaching/learning experience that provides students with problems before they receive any instruction” (Drake & Long, 2009, p. 1). Typically problems are ill-structured, requiring students to work actively and collaboratively in small groups to investi- gate, pose questions, gather information, and carry out the work necessary to resolve the problem. Students engaged in PBL “increase knowledge and develop understanding by identifying learning objectives, engaging in self-directed work, and participating in discussions” (Barrows & Tam- blyn, 1980, as cited in Wong & Day, 2009, p. 627). Five of the nine studies reviewed (Akınoğlu & Tandoğan, 2006; Chen & Chen, 2012; Drake & Long, 2009; Potvin, Mer- cier, Charland, & Riopel, 2011; Wong & Day, 2008) ground their definition of PBL in the medical education **literature** by Barrows (1986, 1996) and Barrows and Tamblyn (1976, 1980). In contrast to traditional instruction where students apply concepts and principles to real-world applications at the end of a unit, problem-based instruction according to the clinical medicine tradition provides students with

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After an initial search of the relevant **literature** on fractions and student proficiency, I identified several skills, conceptual understanding, and student traits that had previously been researched and analyzed within the education community in relations to success in **mathematics** at all K-12 grade levels. The **literature** also revealed two possible categorizations of these skills based on their analyzed effectiveness: conceptual understanding and student traits. These two categories are differentiated given that the first (conceptual understanding) can be categorized as cognitive skills, the “ability to process…, reason, remember, and relate”(“Cognitive Learning Approach | Oxford Learning®,” n.d.) information, whereas the second (student traits) can be classified as non-cognitive, a set of attitudes, behaviors, and strategies. These categories then led me to consider the effectiveness of the individual conceptual understanding and student traits for the purpose of early intervention.

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Research indicated that using children's lit- erature in teaching mathematics contributed to reduced math anxiety among students and bet- ter linkage ofreal world mathematics with cla[r]

A case study in an elementary school in Ohio (Foshay, 2002) gathered data on student achievement gains after three years. Of the 88 participating students, 84% were Black and more than half came from low-income families. They were students in grades 3-5 Title I math classes, which were taught using a traditional elementary curriculum in a block scheduling structure. Students would use PLATO as primary instruction for 30 minutes, and then rotate into small groups with teacher supervision for another 30 minutes. The measure used was the Ohio State Performance Test for **mathematics**.

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From this Literature review the reader should have gotten a very good overview of the aspects of the human auditory system that contribute to hearing and those that may be affected in th[r]

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The use of context in **mathematics** test items is now accepted practice in many forms of national assessment in the UK, with, on occasion, as many as 50% of questions in a particular set of papers involving some mention of a context external to **mathematics**. Yet that the use of context is not entirely straightforward is borne out by research. For example, Silver, Shapiro & Deutsch (1993) researched the now famous ‘bus’ item, reporting how children, when asked to work out how many 36- seater buses would be required to transport 1128 soldiers, included fractions of a bus in their answers. Similarly, Verschaffel, De Corte & Lasure (1994) found that children can fail to apply realistic considerations to their solutions of word problems. In the UK, Cooper and Dunne (2000) studied National Curriculum test items for **mathematics** at Key Stage 2 (when pupils are 11) and, while they found a similar range of ‘misinterpretations’ as Silver et al and Verschaffel et al, they, interestingly, carried the analysis a stage further by looking at responses in relation to family social class. What they concluded was that the way children applied mathematical procedures was subject to class bias, implying, for Cooper and Dunne, that National Curriculum test items are unreliable. An alternative explanation might be that the test items analysed were flawed in the sense that the degree of realism brought to each item by those taking the tests invited a range of responses that were not taken sufficiently into account by the assessment mark schemes. This raises the issue of the nature and degree of ‘realism’ presented in assessment items and what influence this might have on the range of responses obtained. While this existing research seems relevant to the situation in A-level **mathematics**, in surveying the **literature**, no equivalent research appears to have been carried out in relation to the use of context in post-16 examinations.

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TSM only teaches how to do this by rote, because slope is defined in TSM as the difference quotient of the coordinates of two given points on the line. The education **literature** follows suit and concentrates on finding great pedagogical strategies to teach slope according to this misleading definition.

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Katipunan Avenue, Loyola Heights, Quezon City 1108 Master in English Language & Literature Teaching (with Thesis) Ph.D. in English Language and Literature[r]

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The **literature** on (EC) is extensive. Key items include many of Dummett’s writings, together with contributions by Tennant and Wright, among others. Sample references: Dummett [36], [37], [38]; Tennant [139]; Wright [148]. these two readings is illicit, because, after all, the domains of reasons for belief with which they operate were characterized by appeal to the absolutist domain of reasons for belief. (For a given region of thought first the absolute domain of reasons for belief was characterized, and then the relativized domain of reasons for belief was characterized by imposing certain restrictions on it. On the open-ended reading, there was a range of relativized domains of reasons.) This is not a very strong objection. It is correct that they were initially introduced as being obtained from the absolutist domain of reasons in some way or the other. However, the appeal to the absolutist domain of reasons is dispensable. It is more interesting to note that the absolutist reading is not essentially realist. I have chosen to adopt propositions as reasons for belief and as that in terms of which it is determined whether or not clause (ii) is satisfied. On the absolutist reading the facts determine what propositions are true, and, in turn, the true propositions determine whether or not clause (ii) is satisfied for a given entitlement candidate. The observation to be made here is that the notion of fact or truth can be made to accord with one’s philosophical outlook. The facts can be taken to be mind-dependent - rather than mind-independent - and truth can be conceived as being epistemically constrained.^^

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Similar considerations can be drawn regarding the relationship between time pressure and emotional aspects within the mathematical learning framework, leaving space for several open questions. Among them is whether time pressure can be always considered as a negative factor in terms of proficiency and math anxiety. To date the **literature** does not clearly answer this issue. Decreased performance under time pressure is not consistently observed in high or low math anxiety individuals. Previous problem-solving studies suggest that time constraints inhibit creative thinking; but more recent research indicates that time constraints can sometimes prove beneficial (Medeiros et al., 2014). An alternative explanation of this inconsistent pattern may be found in the social pressure **literature** by considering where individuals focus their attention during the performance. It may be important whether attention is directed on the process of performance or to the outcome of performance: these situational aspects of the attentional system may affect results. Pressure does not simply cause a reduction in executive resources; it changes one’s motivational state, leading to failure or success with different types of tasks due to the availability of attentional resources during performance (see e.g., Markman et al., 2006; Worthy et al., 2009).

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_Launched in 1997, with the particular purpose of raising standards in early numeracy as well as literacy, Early Intervention 1998-2000 (HMI, 2001) reports the programme to be successful. However, there are few documented evaluations of the Programme with respect to numeracy, allegedly because intervention in numeracy is much less well developed than that in literacy. The one notable exception, by Fraser et al (2001), reports no significant improvement in attainment amongst children in Primary 3 between 1998 and 2000. Indeed, attainment in **mathematics**, as determined by Performance Indicators in Primary Schools (PIPS tests), was lower in 2000 than in 1998 in some schools. While this might seem to be disappointing, it is not surprising. Many HMI audit reports attest to the relatively successful start that children make in school **mathematics**. According to the **literature** (for example Nunes & Bryant, 1997 ) most children's early success is attributable to their robust, intuitive

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Gender differences are a recurrent theme throughout the **literature** in academic studies in general and in **Mathematics** studies in particular. **Mathematics** is often considered to be a domain in which boys are higher achievers, both in terms of attitudes and self-concept. Sometimes, **Mathematics** is also considered as very important and largely masculine subject (Ernest, 2004:120). Several studies gives evidence that compared to boys, girls lack confidence in doing Mathematical sums and viewed **Mathematics** as a male domain. The role of gender in influencing Mathematical achievement is a very controversial issue. A study conducted by Moreno and Mayer (2009:356) on gender differences in responding to open-ended problem solving questions suggest that males perform better than females on solving a problem (Ernest, 2004:120). This is supported by Fennema’s (2005:304) findings (2009:236) that males perform better than females when tasks involve the cognitive skills used in **Mathematics**. The above findings are corroborated by the studies conducted by Gallagher and Lisi, (2004:205) and Patterson, Decker, Eckert, Klaus, Wendling and Papanastasiou, (2003:93) which revealed that male students are able to solve implicit problems and problems that do not require specific strategies because they have a more positive attitude towards **Mathematics** than female students.

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Therefore, it was not shocking when in 1977 we found that Partial Differential Equation was a subject for a degree programme at the Faculty of **Literature**, Université Paul Valéry, Montpellier, France. In France, **mathematics** is a way of life. Look at the statement of their Minister of Education in Science of June 1998 edition. He said: “La France est la terre des mathématiciens (France is the land of mathematicians).” There, we can hear student, teacher, and lecturer say that **mathematics** is the science of all possible worlds. In India, students consider **mathematics** as the mother of technology. What is our vision? Actually, whatever our vision is or our description of **mathematics** is, it reflects our soul, mindset and spirit.

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This study, unlike the other experimental studies conducted in this field, provides a unique contribution to the teaching math creativity **literature** in terms of using lots of creative techniques together and for the first time. These techniques can be exemplified as origami, tangram, brainstorming, thinking aloud, problem solving by using specific objects (for example toothpicks and paper), naming figures discovered, tree diagram, analogy, story, and drawing. Also, it contributes to the limited **literature** in this field by showing that, in addition to the other studies’ outcomes, creative techniques have an effect on the math anxiety, as well. This study is limited to the subjects of polygons and ratio, and 6 th grade students. Therefore, the findings of this study can be generalized to this grade level and to these subjects. Further studies can offer opportunities to handle teaching math creatively by focusing on different subjects and class levels. Moreover, this study has a geographical and sample size limitation. It is only limited to 42 students studying at elementary schools in Denizli city’s central county, Turkey. Future studies can be conducted in other cities in Turkey and abroad with a larger sample group. This study, however, is limited to 28 class hours. The long term effects of teaching math creatively on academic achievement, attitude, and anxiety can be observed by increasing the duration of experimental procedure. Moreover, this study makes use of experimental design. Research designs based on qualitative design (observation, interview) can be used in further studies in order to characterize the changes brought about during the experimental procedures in a more clear and detailed way and in order to collect data in a deeper manner.

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In lessons Lindsay used contexts for questions that she believed would relate to students’ lives and interests. These included tasks about the calories in burgers, alcohol consumption in England and the cost of smoking. Occasionally the context was linked to the students’ vocational course. Although Lindsay was careful to use current prices and authentic sources of information, the mathematical calculations involved in these tasks often seemed unrelated to anything the students would realistically want to work out in that scenario. This was not a concern for Lindsay because her strategy was to engage the students in the lesson through discussion about the context or scenario, even when this deviated from **mathematics**.

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(ii) All queries If your problems require lengthy discussions then you should attend the **Mathematics** Workshop (MATH3075). This runs throughout the teaching year, in Eustice J (5/2017), from 15.00 to 18.00 each Monday and Wednesday. It is staffed each afternoon by two tutors and a few copies of the course texts are available for consultation. The Workshop is there principally to support this course but it can also be used by any other student in the University with mathematical queries. The Workshop has proved an extremely useful facility for first and second year engineering students. If you experience difficulties during the year, or your mathematical background is weak or rusty, then you are strongly advised to make use of the Workshop. You can drop in any time it is open, for five minutes with a quick query, or go along for the full three hours each session and work through the week’s Module with help readily available when you get stuck. It is there to help you. Use it.

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Standard Four: Knowledge of Content : The elementary teacher is knowledgeable, in addition to literacy and **mathematics** in the following content areas: civics, economics, foreign language, geography, history, science, music, visual arts, and physical education. Middle school and secondary content teachers shall be knowledgeable in literacy and **mathematics** and expert in their content endorsement area(s).

This course is designed to provide students with the opportunity to explore the uses of **mathematics** and computer programming as tools in creating effective solutions to complex problems. Students will develop and refine fundamental skills of computer science within a mathematical context. Computer Science and **Mathematics** may be counted as a fourth math credit course under Smart Core. Any reference to an algorithm or algorithms in this document includes both **mathematics** and computer science contexts. Throughout the course, students will use developmentally appropriate and accurate terminology when communicating about technology. Teachers are responsible for including the eight Standards for Mathematical Practice found in the Common Core State Standards for **Mathematics** (CCSS-M). Computer Science and **Mathematics** does not require Arkansas Department of Education approval.

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This paper aims to give a general overview of industrial **mathematics** applied to papermaking. Modelling challenges vary from computational ﬂuid dynamics (CFD) to ﬁnite-element analyses (FEA) when the paper web transforms from a multiphase ﬂow to a solid ﬁbre network - to a ready paper. Also, diﬀerent length scales are present from ﬁbre level to machine level problems, i.e. from millimetres up to one hundred metres. Mathematical modelling of papermaking is aiming at optimizing the process and the end-product. Thus, computational tools for optimal shape design and optimal control purposes have been developed.

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Through the use of abstraction and logical reasoning, **mathematics** developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical **mathematics** has been a human activity as back as written records exist. Rigorous arguments first appeared in Greek **mathematics**, most notably in Euclid's Elements. **Mathematics** developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.

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