This collaborative project between Morehead State University, Northern Kentucky University, and the University of Kentucky provides information about the extent to which an innovative learning experience focused on the professional noticing of children's numeracy develops preservice teachers' (PSETs') capacity to attend to, interpret, and respond appropriately to the mathematical thinking of children. The project uses a module, Noticing Numeracy Now (N3), developed by the researchers and based on professional literature in the areas of professional noticing and the Stages of Early Arithmetic Learning (SEAL). The research advances knowledge and understanding of how teacher educators can facilitate PSETs' development of professional noticing, knowledge of children's conception of unit, mathematical knowledge for teaching, and positive attitudes toward mathematics. The activities present a creative and potentially transformative approach to the preparation of future elementary teachers through classroom and field activities that explicitly promote the development of the component skills of professional noticing in the context of SEAL.
The Noticing Numeracy Now (N3) module, designed for replication, is being implemented at six universities, the three lead institutions along with Eastern Kentucky University, Murray State University and the University of Louisville. The student populations at these institutions represent cultural and socio-economic diversity, including underrepresented groups. Collectively, the six universities draw their student populations from culturally diverse, urban populations and predominately Appalachian rural populations. Many of the students are the first in their families to study at a university.
The intent of this study was to measure the professional noticing skills, attitudes and beliefs toward mathematics, and mathematics knowledge for teaching for preservice elementary teachers involved in a unique learning experience. Each of the participating researchers taught a unique multi-session module in their elementary mathematics methods courses that embedded the Stages of Early Arithmetic Learning (SEAL) within a module intended to develop professional noticing skills. Pre- and post- measures were collected for each of the variables being studied and analyses are continuing to be studied on those variables and their relationships. Initial smaller sets of data have been analyzed for this report; however, data analyses is an ongoing process and there is more data to be studied. Professional Noticing (Initial data, n = 94) A Kruskal-Wallis test was conducted to determine whether there was a statistically significant difference of the changes of the scores from pre-test to post-test between the universities and those changes were not found to be significant in attending (χ2 = 2.022, df = 2, p = 0.364), interpreting (χ2 = 0.541, df = 2, p = 0.763), or deciding (χ2 = 0.837, df = 2, p = 0.364). Despite the significantly lower starting score for deciding at University A, the lack of significance in the changes of the scores between universities indicates that all universities are growing at the same pace and the instructional module has a similar impact on the prospective elementary school teachers at the various institutions involved in the study. Therefore, subsequent analyses and discussion will focus on the entire group of participants instead of stratifying by university. A Wilcoxon Signed Ranks test was conducted for each of the three questions to determine whether statistically significant gains were found for each component of professional noticing (attending, interpreting, and deciding). Statistically significant increases were found in all three components with deciding having the strongest increase. With lower pre-assessment scores, deciding had more room for growth. Attitudes Toward Mathematics (Initial data, n = 123) Paired t-tests were applied to ATMI data to examine PSET change in attitude toward mathematics from pre-assessment to post-assessment. There were statistically significant increases in the enjoyment, self-confidence and motivation factors. There was not a statistically significant change in the fourth factor, value, when all 123 cases were included. However, when the 15 cases that achieved the maximum possible score on the value factor on the pre-assessment were removed, there was a statistically significant increase in this factor from pre- to post-assessment (t = 2.181, p = 0.031). Mathematics Knowledge for Teaching (Initial Data, n = 166) When the overall means of the pre and post LMT assessments were compared, it was revealed that the overall mean of the LMT decreased. When they were compared to determine if there was a statistically significant decrease, a paired samples t-test revealed that this decrease was not statistically significant (t = 1.113, df = 165, p = .267). Relationships Between Professional Noticing and Attitudes Toward Mathematics (Initial data, n = 123) Spearman’s rho correlations were employed to examine the correlation between the change in professional noticing and the change in attitudes toward mathematics. While significant PSET growth was found in all three professional noticing components and in three of four factors of the ATMI, there was no statistically significant correlation between changes in professional noticing and changes in attitudes toward mathematics at the component/factor level or when overall scores of both professional noticing and ATMI were analyzed (rs = -.020, p = .828). Relationships Between Professional Noticing and Mathematics Knowledge for Teaching (Initial data, n = 166) In order to determine if there is a correlation between the changes in the components of professional noticing and the LMT scores, a spearman’s rho correlation was calculated between the overall change score on the LMT and each of the three professional noticing components. One comparison that yielded a statistically significant correlation (at the p = .05 level) was the correlation between the change in LMT and the change in the deciding component of professional noticing (rs = .155, p = .047). Further analyses of professional noticing and LMT revealed that there existed a statistically significant correlation between the post-assessment scores for the attending component of professional noticing and LMT (rs = .170, p = .029). NOTE: Further analyses with the entire data set and additional correlations are still being calculated and will appear in future publications from this project.
