- MyMaths - Bringing maths alive - In secondary schools
- C'est pratique
- Teaching Mathematics: A Handbook for Primary and Secondary School Teachers
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MyMaths - Bringing maths alive - In secondary schools
Add to Compare. The problems and exercises in these books encourage students to think creatively to be flexible in the use of new ideas and approaches to be fluent in the creation of an array of ideas to elaborate on similar ideas to be original in thinking of new approaches or new ways of seeing problems.
What are the famous Korean researchers, what kind of explanations do they give us about where the origin of strong dominance of content knowledge comes from? One common explanation is, of course, Confucian Heritage Culture, which sees a teacher as an expert, as a scholar-teacher.
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Relationships between U. Progressive education with child-centered approaches dominates in Scandinavian countries, and especially in North and South America, and countries shaped by American influences, for example, the Philippines and Singapore Nebres, Content is more in the background, although not totally in the background.
Anglo-American countries have a tradition of pragmatism Kaiser, When it comes to mathematics teaching, argumentation and proof is less important than in European traditions. Mathematical structure is less important in syllabi and daily teaching. Compared to English-speaking countries, this broader, theory-guided knowledge has a very close connection to the subject of mathematics. Generally speaking, didactics is a constitutive element of continental European educational approaches Pepin, Its epistemological character, that is, the central focus on specific knowledge in a different form, and the conditions for enabling pupils to acquire it.
Its actual and potential roles in relation to teaching and teachers in particular, didactics as a design science and as a part of teacher education and the professional knowledge base. These kinds of aspects are very apparent and important when it comes to didactics and its traditions. These educational orientations influence curricula. In European curricula, the very strong normative orientation influences their structure: There is a long preamble with normatively based goals of mathematics education.
There is a strong subject orientation. In the upper secondary level, calculus is compulsory in Germany. There is an intensive focus on argumentation and proof. Continental European curricular traditions and Korean curricula have a remarkable relationship, in contrast to American traditions, amongst others. There are similar pillars in the new Korean curriculum for the lower secondary level Lew et al.
There is a strong focus on mathematics content in traditional and innovative classrooms e. There are intensive reflections on the learning of proofs and their gradual development Kim and Ju, There is a strong focus on content knowledge in teacher education curricula Kwon and Ju, Kaiser concluded that these reflect commonalities in didactics of mathematics in Europe and Korea.
Mary Kay Stein began by noting that there are two broad kinds of standards in the United States. As noted earlier, the NCTM started the standards movement for mathematics and other subjects with the release of the Curriculum and Evaluation Standards for School Mathematics. As mentioned earlier, the NCTM cannot mandate adoption of its standards. In that act, each state was required to establish standards for what students should know and be able to do, and to create assessments for measuring their attainment of those standards.
Unlike the NCTM standards, state standards have the force of law. As the NCLB law stands now, all students must have been proficient in mathematics by the spring of , or sanctions would have been applied. This was in reaction to the state standards; many of them had become quite bloated as a result of the NCLB law. A commonly heard description of the U. This is supposed to make it easier for teachers to communicate with each other, and with students, principals, and parents.
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Higher refers to more demanding content. Together these three features should, theoretically, set up teachers to spend more time helping students to understand more deeply a smaller set of goals for each grade level. Stein commented that she thought that her U. A second feature is that the CCSS aim to develop understanding over time. They do this by defining a set of K—12 pathways that students must be on to meet standards for college and career readiness by the end of high school.
The pathways, in turn, are rooted in a set of learning progressions. July 1, The idea is that the teacher will be helped by the two new assessments that are being developed. The hope is that these assessments will give not only a summative evaluation at the end of each year but also formative evaluation along the way, providing reports to teachers about whether their students are on the pathway or falling behind. A third distinguishing feature is the positioning of the standards for mathematical practice SMPs.
While agreeing that there is some continuity in the substance of the SMPs, Stein argued that there were also some discontinuities. She noted the relative isolation of the SMPs from the content. Compared to past standards, the practice standards are not integrated with the content standards, are less well specified, much less specific than the content standards, and the same across grade levels. This limited guidance from the CCSS regarding how to integrate the standards for practice with the content standards is a concern. In its absence, guidance will be left to textbook publishers, Stein said.
A related concern is that assessments will not give as much weight to practice standards as they do to the content standards.
In that case, teachers will get the message that the practice standards are secondary to the content standards. The fourth feature is the commonness of the Common Core. A related concern is political forces, which continue to challenge the Common Core on the basis of the U. Another concern is the equality of opportunity that is supposed to emerge from these common standards. It will not materialize on its own. Instead, it will require the commitment of state departments of education, resources, and the professional development of teachers. Stein briefly mentioned two issues related to implementation of the CCSS: 1 instructional programs that can support the transition to the new standards and 2 assessments of the new standards.
She reminded the audience that it was the summer of , and there would be two full school years before the assessments would be administered in — How would schools handle this transition period, especially at the instructional program level? Ideally, this coherent instructional system would spring into place full blown at the moment that it was needed.
Instead, schools and districts are scrambling to not only build and enact instructional systems but also to assure that students get help if they are not ready for the grade-level knowledge and skills that will be taught. The two assessment consortia have been laboring for the most part behind closed doors, yet much depends on these assessments.
Past experience suggests that teachers will pay the most attention to the assessments once they are released, and the standards will recede into the background. Teachers will teach to the assessments, and the curriculum will narrow to what is tested. The claim is that teaching to the test—with the Common Core test—will be a good thing, because it supposedly will represent higher, more demanding kind of content and more performance-based activity. Past experience suggests that without additional professional development, teachers will imitate the form of assessment items, but not their substance.
A second concern is, Will the assessments yield student data that is useful for guiding teachers? Hawaii has been doing in-service work related to the CCSS for the past year and a half. Historically, Hawaiian elementary teachers have relied heavily on textbooks. After the CCSS were released, teachers still used their old textbooks, which were not aligned. This poses a great problem for teachers that do not have the necessary mathematical content knowledge. Professional development is another challenge. There are more than 13, teachers in the state of Hawaii, on several islands.
Approximately 9, teach mathematics.
Teaching Mathematics: A Handbook for Primary and Secondary School Teachers
Many Hawaiian teachers are not tech savvy and not used to having professional development material delivered by video, webinar, webcasting, or other online tools. The CCSS are very different from the current state standards. Previously, Hawaiian standards changed only slightly from version to version. Although the NCTM process standards should have been a part of classroom teaching, teachers sometimes did not know what the process standards were because they appeared at the very end of the Hawaiian document.
The new CCSS give the standards for mathematical practice in the front of the document. The CCSS are very specific about content at each grade.
Because of this, some teachers need help in realizing that their favorite topic or unit may not fall within the standards for their grade. Stacie Kaichi-Imamura described the situation with textbooks. Publishers have not yet created aligned textbooks.