Scooter Nowak, Michigan State University Amanda Opperman, Michigan State University Amy Parks, Michigan State University. On behalf of the 2015 PME-NA Steering Committee, the 2015 PME-NA Local Organizing Committee, and Michigan State University, we welcome you to the 37th Annual Meeting of the International Group for the Psychology of Mathematics Education - North American Chapter of held on the campus of Michigan State University in East Lansing, Michigan.
Chapter+1+
Plenary+Papers+
They can immediately notice that two Lengths A = second object and that two Lengths A = Length B. Many are called but few are chosen”: the role of spirituality and religion in the educational outcomes of “chosen” African male mathematics majors - Americans. .
Making(and(selling(candles
Based on examples of students' work produced during the lesson, the teacher draws attention to important concepts that have emerged (e.g. the connection between speed, slopes in graphs and differences in tables). Sequence the distribution of sample student work so that sequential pairwise comparisons of approaches can be made;.
Chapter+2+
Special+Session++
This session will provide information on current funding opportunities for mathematics education research and development from the National Science Foundation. Currently, the National Science Foundation has a number of programs in the Directorate of Education and Human Resources that provide opportunities to fund research and development in mathematics education in K-12, undergraduate, and graduate education.
Chapter+3+
Curriculum+and+Related+Factors++
Noticing Curricular Task Design Features
Study 1 examined the task design features that PSTs in secondary mathematics pay attention to. PSTs (n = 8) in two groups were given one of two versions of the same challenging optimization task, with each version reflecting common presentations in textbooks. After each group had worked together on their version of the task for 10 minutes, the whole class discussed the math challenges they encountered and the strategies they used.
The whole class held a discussion about the differences they noticed between the two versions of the task. While the mathematical goal of the task (solving for an optimal value) and the context (placing a stereo in a cabinet) were the same, the way the task prompted students to engage resulted in differences. Some prospective teachers were concerned about how the design of the task could "obscure" important mathematical ideas. the scope of their work depended on the version they were using.
Noticing Mathematical and Pedagogical Opportunities in Curricular Tasks
The groups that began the open-strategy task reported testing the item to see what it would tell them, while the closed-strategy group was restricted to the intention of following instructions. For example, one task specifically asked "how can you be sure you found the best answer?" while the other just asked for an answer. They observed that when a strategy is given, the group works in parallel and limited discussion to checking the answers or how to carry out the procedure.
They also noted that the ability to discuss with the entire class was significantly increased when multiple strategies were supported.
Using a Tool to Examine PSTs Attention to and Interpretation of Curriculum Materials
Following this analysis, PSTs answered the same questions from the beginning of the semester. After using the CCCAT, their evaluations were more detailed and they described different aspects of the materials. Six of the top 10 reasons were explicitly aligned to aspects that PSTs were asked to use when evaluating texts using the CCCAT.
They also commented more on the ways technology was integrated, meaning whether it appeared to be an integral part of the text, rather than just naming what tools were used in the text. In addition, however, the PSTs also discussed aspects that were not explicitly analyzed in the CCCAT. While potentially useful for applying the CCCAT, these aspects were not explicitly addressed, meaning that PSTs were not asked to address these aspects in the same way as the others.
Responding with Curricular Materials
Previous research has identified one of the dominant factors contributing to the complexities of teaching and learning fractions lies in the fact that fractions constitute a multi-layered construct (Lamon, 2007). In the third grade, the focus is on the continued development of fraction concepts together with the introduction of adding and subtracting fractions with the same denominator. In fact, none of the assessments for the course were directly related to the textbook.
Also disturbing was that the students expressed a persistent concern about the correct formatting of the online homework answers. Thirty-three of the tasks were coded as procedure with connections (23%), while only 3 were coded as doing math (2%). For example, the teacher's role in the launch is to assess students' prior knowledge and relationship to the problem challenge.
TH GRADERS’ MATHEMATICS SUCCESS ON TIMSS IN RELATION TO NATIONAL HIGH SCHOOL PLACEMENT TESTS
Studies conducted in the second half of the twentieth century in many different languages and cultural norms have found that the semantic structure of word problems influences difficulties in young children, and word problems have been organized into taxonomies based on semantic structure and difficulty. (Fuson, 1992; Verschaffel, Greer, & DeCorte, 2007). Currently, the Common Core State Standards for Mathematics (CCSSI, 2010) specifically include the full range of word problems found in established taxonomies. Do the textbooks used in the classrooms of the students in our sample offer different learning opportunities in terms of the semantic structure of the text tasks than the textbooks used in the classrooms of the students in the 1970s and 1980s samples?
The participants were interviewed individually and completed two surveys at the beginning and end of the project in the academic year. Participants were satisfied with the math content, the use of technology for teaching and communication, and the assessment activities carried out in the program. The findings of this curriculum content design program can be used in similar educational contexts.
Chapter+4+
SS: How many cubes did you bring in all?
That is, he seemed to have made a figurative mental template of the size of each compound unit. Since counting by 5s was within his ability, his increment count—which he demonstrated to the teacher—indicated a purposeful method of keeping track of the number of units assembled so that he knew to stop at four towers. This seemed to support his growing anticipation of the connection between coordinated actions to compute a progressive total and the effect of stopping the count of 1s upon reaching the number of compounded units (which fits his statement: "I have brought 4 towers").
It is important to consider the purpose of the teacher's interventions (e.g. "how did you count"). By asking Jak to explain, she was thus trying to direct his reflection and awareness of his own purposeful actions (eg, he was following assembled units). First, she focused Jake's attention on a particular aspect of his coordinated counting—tracking compound unit billing.
Finding the total number of cubes in 5 towers of 2 cubes each Nina: Can you show me?
A child can initiate and carry out goal-directed actions while not being aware of his own actions, let alone the steps he has taken to monitor those actions. To explain his strategy, Jake used fingers, which the teacher intended as a way to promote two critical reflections in the construction of the mDC scheme. In the next PGBM task in which Jake played the bringer, he had to figure out and explain how many cubes are in 5 towers with 2 cubes each.
Again, Nina asked for his explanation of his solution, as his answer (10) came after nodding his head silently five times, but without using his hands/fingers.
Jake: I brought 11 cubes altogether
Jake: (He folds 4 fingers on his left hand, then curls a finger on his right hand; repeats the process for the second and third towers, while the fingers of the left hand appear to represent 1 and the fingers of the right hand appear to represent compound units/towers.). He folds three fingers on his right hand, one after the other as he speaks) This is the first tower, this is the second tower, and this is the third tower. With his left hand, he drops one of the fingers on his right hand and says "Four." Then he raises his left hand, counts four fingers and says.
Nina: And you knew to stop at 12 because these were like the towers (he touches the fourth finger on his right hand and this was like the 12th. In an "oops" moment, he realized that counting the reappearances of the figurative tower in .the right hand wasn't moving toward his goal and started over.On his second try, Jake was able to accurately use his fingers to keep track of the unit rate of 4.
Nina: How many cubes did you bring altogether?
Due to lack of ease with the next two multiples of 4, reverted to using left hand counting accrual 1s, keeping track of compound units with fingers on right hand. On the contrary, when a change in the child's way of functioning is to be promoted, such as the cognitive shift from additive to multiplicative reasoning (Steffe, 1992), the initial emphasis in task design and implementation should be placed on targeting the child's mental powers. the novel. To this end, the choice of 'easy' numbers seems very productive, because the child can bring available knowledge of numerical calculations with which he or she seems easy (eg, multiples of 2s and 5s).
Initially solving tasks involving 'easy numbers' enables the child to construct the intended goal-directed activities (a new scheme) which can then become an immutable way of functioning that she or he could use to solve tasks with numbers that require engaging more complex mental capacities. The scope of this paper did not allow us to provide data on how this change was successfully promoted in Jake after what we have seen in extract 4.). Specifically, we showed how Jake was able to use his newly developed understanding of the coordinated counting of compound units and begin to operate in multiplicative situations when using 'easy numbers' (Excerpts 1 & 2). -back can thus also be a good indicator of the need to pay close attention to the child's conceptualization, in the following threefold sense:. a) not simply ascribing to the child too high a level of conceptual growth because of success.
