Our revised secondary teacher education professional development plan (PDP) project required pres... more Our revised secondary teacher education professional development plan (PDP) project required preservice teachers to identify their teaching beliefs, use these beliefs to analyze practice, and create an action plan centered on a research question from this analysis. We predicted these plans would show evidence of reflective dispositions (open-mindedness, whole-heartedness, responsibility). We had two research questions to examine this assertion: 1) To what degree did our pre-service teachers' PDPs show evidence of Dewey's dispositions toward reflective practice? 2) What were the trends for each of these dispositions? Overall, the PDPs showed evidence of all reflective dispositions; however, the dispositions were unevenly represented. From this study, we recommend a more longitudinal and personalized approach to the PDP to make it more integral to the development of preservice teachers.
This proposed research investigates a particular phenomenon that occurred during a study of stude... more This proposed research investigates a particular phenomenon that occurred during a study of students' flexibility in solving linear equations (Star, 2004). 160 6th graders participated in five hours (over five days) of algebra problem solving. In the first hour, the students were given a brief lesson on four different steps that could be used to solve algebraic equations (adding to both sides, multiplying on both sides, distributing, and combining like terms). Students then spent three hours solving a series of unfamiliar linear equations with minimal facilitation. 23 students (randomly selected from all participants) were interviewed while working individually with a tutor/interviewer. On the last day of the project, students completed a post-test.
This article compares the opportunity to learn length measurement in the USA and Singapore as rev... more This article compares the opportunity to learn length measurement in the USA and Singapore as revealed in the close analysis of some of their written elementary curriculum materials. Written curricula strongly influence students' learning of mathematics, without completely determining it. The Trends in Third International Mathematics and Science study 2007 showed the relatively low performance of the US and Singapore fourth graders in measurement, which was attributed in part to the learning opportunities provided to the students. We examined and coded all instances of length measurement in three different US curricula and one Singapore curriculum through Grade 3, using a very detailed scheme that identified particular elements of conceptual, procedural and conventional knowledge and the textual forms that present this knowledge. Results show strong emphasis on measurement procedures, across all grades and curricula, in both countries. However, in numerous ways, the Singapore curriculum is more focused, organizationally, procedurally and conceptually. US curricula provide more diverse access to conceptual knowledge where Singapore materials focus on independent work involving procedures, within and across grade levels. Limitations of the curricula in both countries are discussed.
ABSTRACT This study explored students' perceptions of self-directed learning (SDL) and co... more ABSTRACT This study explored students' perceptions of self-directed learning (SDL) and collaborative learning (CL) with/without technology in an information and communications technology-supported classroom environment. The factors include SDL, CL, SDL supported by technology, and CL supported by technology. Based on the literature review, this study hypothesized that students' perceptions of learning without technology positively predict their perceptions of learning supported by technology. An instrument was developed and two studies, a pilot study and a main study, were undertaken. The pilot study surveyed 219 secondary school students and established the factors through exploratory factor analysis with good validity and reliability. The main study surveyed 500 secondary school students to confirm the factors and to establish the relationships between these factors through structural equation modeling. The results validated the four-factor structure model and revealed that students who reportedly engaged in SDL and CL in face-to-face contexts also engaged in these forms of learning in technology-supported contexts. The findings indicate that students' learning without technology support is related to their use of technology for learning. It may be advisable for teachers to develop students' learning processes in the face-to-face context without technology before engaging them in technology-supported learning.
This proposed research investigates a particular phenomenon that occurred during a study of stude... more This proposed research investigates a particular phenomenon that occurred during a study of students' flexibility in solving linear equations (Star, 2004). 160 6th graders participated in five hours (over five days) of algebra problem solving. In the first hour, the students were given a brief lesson on four different steps that could be used to solve algebraic equations (adding to both sides, multiplying on both sides, distributing, and combining like terms). Students then spent three hours solving a series of unfamiliar linear equations with minimal facilitation. 23 students (randomly selected from all participants) were interviewed while working individually with a tutor/interviewer. On the last day of the project, students completed a post-test.
ABSTRACT Extensive research has shown that elementary students struggle to learn the basic princi... more ABSTRACT Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students’ difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K–3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3.
Extensive research has shown that elementary students struggle to learn the basic principles of l... more Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students' difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K-3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3.
Our revised secondary teacher education professional development plan (PDP) project required pres... more Our revised secondary teacher education professional development plan (PDP) project required preservice teachers to identify their teaching beliefs, use these beliefs to analyze practice, and create an action plan centered on a research question from this analysis. We predicted these plans would show evidence of reflective dispositions (open-mindedness, whole-heartedness, responsibility). We had two research questions to examine this assertion: 1) To what degree did our pre-service teachers' PDPs show evidence of Dewey's dispositions toward reflective practice? 2) What were the trends for each of these dispositions? Overall, the PDPs showed evidence of all reflective dispositions; however, the dispositions were unevenly represented. From this study, we recommend a more longitudinal and personalized approach to the PDP to make it more integral to the development of preservice teachers.
This proposed research investigates a particular phenomenon that occurred during a study of stude... more This proposed research investigates a particular phenomenon that occurred during a study of students' flexibility in solving linear equations (Star, 2004). 160 6th graders participated in five hours (over five days) of algebra problem solving. In the first hour, the students were given a brief lesson on four different steps that could be used to solve algebraic equations (adding to both sides, multiplying on both sides, distributing, and combining like terms). Students then spent three hours solving a series of unfamiliar linear equations with minimal facilitation. 23 students (randomly selected from all participants) were interviewed while working individually with a tutor/interviewer. On the last day of the project, students completed a post-test.
This article compares the opportunity to learn length measurement in the USA and Singapore as rev... more This article compares the opportunity to learn length measurement in the USA and Singapore as revealed in the close analysis of some of their written elementary curriculum materials. Written curricula strongly influence students' learning of mathematics, without completely determining it. The Trends in Third International Mathematics and Science study 2007 showed the relatively low performance of the US and Singapore fourth graders in measurement, which was attributed in part to the learning opportunities provided to the students. We examined and coded all instances of length measurement in three different US curricula and one Singapore curriculum through Grade 3, using a very detailed scheme that identified particular elements of conceptual, procedural and conventional knowledge and the textual forms that present this knowledge. Results show strong emphasis on measurement procedures, across all grades and curricula, in both countries. However, in numerous ways, the Singapore curriculum is more focused, organizationally, procedurally and conceptually. US curricula provide more diverse access to conceptual knowledge where Singapore materials focus on independent work involving procedures, within and across grade levels. Limitations of the curricula in both countries are discussed.
ABSTRACT This study explored students' perceptions of self-directed learning (SDL) and co... more ABSTRACT This study explored students' perceptions of self-directed learning (SDL) and collaborative learning (CL) with/without technology in an information and communications technology-supported classroom environment. The factors include SDL, CL, SDL supported by technology, and CL supported by technology. Based on the literature review, this study hypothesized that students' perceptions of learning without technology positively predict their perceptions of learning supported by technology. An instrument was developed and two studies, a pilot study and a main study, were undertaken. The pilot study surveyed 219 secondary school students and established the factors through exploratory factor analysis with good validity and reliability. The main study surveyed 500 secondary school students to confirm the factors and to establish the relationships between these factors through structural equation modeling. The results validated the four-factor structure model and revealed that students who reportedly engaged in SDL and CL in face-to-face contexts also engaged in these forms of learning in technology-supported contexts. The findings indicate that students' learning without technology support is related to their use of technology for learning. It may be advisable for teachers to develop students' learning processes in the face-to-face context without technology before engaging them in technology-supported learning.
This proposed research investigates a particular phenomenon that occurred during a study of stude... more This proposed research investigates a particular phenomenon that occurred during a study of students' flexibility in solving linear equations (Star, 2004). 160 6th graders participated in five hours (over five days) of algebra problem solving. In the first hour, the students were given a brief lesson on four different steps that could be used to solve algebraic equations (adding to both sides, multiplying on both sides, distributing, and combining like terms). Students then spent three hours solving a series of unfamiliar linear equations with minimal facilitation. 23 students (randomly selected from all participants) were interviewed while working individually with a tutor/interviewer. On the last day of the project, students completed a post-test.
ABSTRACT Extensive research has shown that elementary students struggle to learn the basic princi... more ABSTRACT Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students’ difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K–3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3.
Extensive research has shown that elementary students struggle to learn the basic principles of l... more Extensive research has shown that elementary students struggle to learn the basic principles of length measurement. However, where patterns of errors have been documented, the origins of students' difficulties have not been identified. This study investigated the hypothesis that written elementary mathematics curricula contribute to the problem of learning length measurement. We analyzed all instances of length measurement in three mathematics curricula (grades K-3) and found a shared focus on procedures. Attention to conceptual principles was limited overall and particularly for central ideas; conceptual principles were often presented after students were asked to use procedures that depended on them; and students often did not have direct access to conceptual principles. We also report five groupings of procedures that appeared sequentially in all three curricula, the conceptual principles that underlie those procedures, and the conventional knowledge that receives substantial attention by grade 3.
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