Mathematics Content for Elementary Teachers

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The work is protected by local and international copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. You have successfully signed out and will be required to sign back in should you need to download more resources. Fritzer, Florida Atlantic University. If You're an Educator Request a copy Additional order info.

If You're a Student Buy this product Additional order info. Overview Features Contents Order Overview. Description A short primer on each of the major math content areas that preservice and inservice elementary and middle school teachers are required to know. A great Value pack for students who need to prepare for teacher certification exams. An exhaustive index at the back of the book makes the text a valuable, easy-to-use reference tool.

Up-to-date Websites for each content area are provided to direct the reader to valuable supplemental information. Table of Contents Preface. Sign In We're sorry! Username Password Forgot your username or password? Our hypothesis is that those students who possess higher levels of mathematics competence attainment will have formed different dispositions than those students with low attainment levels. Having teachers with strong discipline knowledge and sound dispositions towards learning seem to be important factors in the literature. There is a view that these negative experiences emerge from personal experiences at school, with a spiralling cycle of adverse perceptions reinforced throughout life Ball, ; Mayers, This is especially important when ill-equipped students encounter higher education mathematics courses, at a level of complexity beyond that encountered at secondary school.

Increasing proportions of these students lacked success at school in mathematics, so the building of their confidence is seen as critical at an undergraduate level. A substantial body of literature has shown that MCK is critical for effective teaching of mathematics Goulding et al. Nevertheless, there is some evidence to suggest that there is a relationship between deep content knowledge and beliefs.

Wilkins , for example, maintained that teachers with high levels of content knowledge were less likely to use inquiry-based approaches in their classroom, rather preferring more traditional methods which presumably worked for them at school.

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As Holm and Kajander postulated, those teachers with weaker mathematics knowledge may be more willing to adopt and embrace recent education practices given their lack of success with teacher-focused instruction. Further, Holm and Kajander , p. By contrast, their PCK should develop throughout their course, due in part to the exposure of professional experiences in the classroom.

2. Mathematics and mathematics education

What do teachers need to know to be good teachers of mathematics? This has been the subject of many studies. Their knowledge and beliefs about mathematics alongside their pedagogical practices have been identified as key factors in quality education. Shulman has been instrumental in creating two clear distinctions in what teachers need to know in terms of their teaching—what to teach the knowledge and how to teach the pedagogy.

In mathematics education, the discipline knowledge has been the focus of considerable debate often with mathematicians focusing on the content knowledge. This knowledge is what Shulman described as subject matter knowledge, or Hill et al. There is a growing recognition that it is increasingly important for teachers to have strong content knowledge in order to be better teachers of mathematics. This is being borne out in current policies e. Matchett, ; Schmidt et al. These contemporary pushes in the field of education recognize the importance for teachers to have strong content knowledge as well as pedagogical knowledge.

Conversely, teachers with poor content knowledge tended to take rather structured teaching approaches where skills were taught in isolation. Generally, however, these alternate perspectives were not commonplace, and the notion that competent teachers produced competent students was posited. Most of the significant studies on content knowledge are quite dated and have been superseded by studies around pedagogy. In part, some of the response to the importance of discipline knowledge was the move in the USA to allow professionals who had discipline knowledge, such as mathematics, to teach with limited pre-service education.

This has also been the source of some contention in Australia with the rollout of the Teach for Australia Teach for Australia, initiative where people with degrees in sought-after areas could become teachers through a very intensive six-week initial course. There is a well-held view that individuals may well possess well-developed MCK but lack the specific types of PCK essential for teaching Hill et al.

In fact, thousands of studies have described the importance of PCK in teaching. As Krauss et al. Similarly, Kleickmann et al. Moreover, these authors have argued that the experience and practice of teaching fosters and develops MCK. This may well be the case when the participants in the study possess relatively well-established conceptual understandings—as may well be the case with a cohort of pre-service teachers attending Cambridge University. It may not be the case elsewhere, especially when considering the mathematics skill base of most potential and current primary school teachers in Australia.

Wu , p. These positions have been supported by the comprehensive work of Hill et al. We suggest that exploring this area of teacher education is valuable as it alerts us to issues within pre-service education that can be addressed prior to teachers entering school contexts. Three research questions are posed, namely: To what extent do SML and age contribute to content knowledge performance?

The Six Guiding Principles of Teaching Elementary Mathematics

The participants in this study consisted of undergraduate students from two universities in Australia—one located in a large rural city and one located in a metropolitan city. The sample was randomly selected from the two tertiary institutions and could be expected to be typical of students from both geographical areas. The cohort comprised second- and third-year students from a four-year programme.

Ridener & Fritzer, Mathematics Content for Elementary and Middle School Teachers | Pearson

All of the students would have experienced at least one, often more, professional placement at the time of survey completion. The second and third sections were timed sections, which supported an effectiveness and efficiency measure. As previously mentioned, this study is concerned with data from section 1 especially student qualifications , section 2 the content knowledge questions and section 4 the affect questions.

The content knowledge section consisted of 11 items sourced from national and international tests designed for middle high school attainment levels. All items were trialled by other researchers or assessment corporations such as Australian Curriculum, Assessment and Reporting Authority, Australian Mathematics Trust, The Mathematical Association of America and Educational Testing Service so that we can assume reliability and validity of the test items, and thus can be used for comparative purposes.

The selection of items was on the basis of ensuring a spread of content areas as well as a range of levels of mathematics. The Beliefs, Values and Attitudes section 20 efficacy questions comprised three distinct parts, namely: All 20 items were on a 5-point Likert scale where participants were encouraged to indicate their views and feelings to questions on a strongly disagree 1 —strongly agree 5 scale.

The SML variable categorized participants into those students who had studied advanced mathematics at school and those who undertook more general courses. In order to score the content knowledge variable, the 11 content knowledge items were categorized according to the syllabus content strands including, Number sense 4 items , Geometry and Measurement 3 items and Statistics 4 items. Means for these categories were calculated for each participant. Table 1 shows the means and standard deviations SDs for mathematics qualification and age across the three content variables.

The means can be interpreted as proportion correct that is, 0.

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Subsequent univariate tests were conducted for the SML variable to determine where the differences were. For each of the three strand measures, those students who undertook higher levels of school mathematics outperformed students who studied more general mathematics. Consequently, we can confidently state that exposure to higher levels of mathematics at school influences substantially general MCK. By contrast, the age at which students enrolled in their teaching degree had no overall effect on their MCK. Although there was no interaction between SML and age, noteworthy descriptive data emerged from the analysis.

The first component of this research question was to undertake an Exploratory Factor Analysis in order to establish interrelationships among the 20 observed variables i. All of the 20 items of the survey could be grouped according to the three factors. The items and factor loadings for the mathematics attitude questionnaire are presented in Table 3. Thus the questionnaire items have high loadings with factors that make conceptual sense.

Mathematics Content for Elementary and Middle School Teachers

Based on these data, the three factors were conceptualized and named in the following manner. This factor comprised three items intended to measure use of concrete materials items 10, 13 and 14 , four items associated with constructing student-focused classroom environments items 5, 6, 8 and 12 and three items associated with connecting mathematics to other discipline areas items 4, 9 and This shared factor indicates that this theme is aligned to a constructivist mentality. Given the mean for this factor, it suggests that most of the participants viewed the constructivist approach in a positive manner.

Three of the items were associated with mathematics being a procedure-based approach items 1, 7 and 20 , with the other two items associated with the notion that mathematics concepts are more easily acquired by certain types of thinkers items 2 and The low mean suggests that most participants disagreed with the notions. The high mean suggests a positive view that discipline strength in mathematics is applicable across other discipline areas items, 3, 15, 16, 17, 18 and