A Logistic Regression Model Comparing Astronomy And Non-Astronomy Teachers In Québec’s Elementary Schools

Based on the results of an online survey of 500 Québec’s elementary (K-6) teachers conducted in 2015 that probed the way respondents teach astronomy to their classrooms, their background in S&T, their pre-service education, their aims and goals for astronomy teaching, their attitude toward teaching astronomy, the resources and materials they use, their view on the effectiveness of preand in-service training, and their need for in-service training, we present a logistic regression model comparing elementary teachers in our survey that teach astronomy to their class (“Astronomy” teachers, N = 244) and those who don’t (“Non-astronomy” teachers, N = 256), to reveal factors that seem to facilitate or hinder astronomy teaching in Québec’s elementary classrooms. Based on the model, several ways to enhance the teaching of astronomy in Québec’s K-6 classrooms are proposed: offer high-quality preand in-service training in astronomy to elementary teachers, raise the profile of science teaching in elementary schools, and help teachers realize the importance of teaching astronomy in their classrooms to cover the curriculum standards.

In the first section of this paper, we will review past surveys that probed science and astronomy teachers in Canada and the United States. These surveys informed the theoretical framework as well as many practical aspects of the construction of our own survey. Then, we will present a brief description of the survey instrument used in the present study, as well as a summary of the major findings of the survey already presented in Chastenay (2018). Finally, we will describe the construction of a logistic regression model comparing Astronomy and Non-astronomy teachers and present the major results. In conclusion, we will propose a series of recommendations, based on the model, to improve and enhance the teaching of astronomy in Québec's elementary schools, hoping that these proposals will be of use for science educators, teachers' trainers and curriculum developers in other parts of the world as well.

PAST SURVEYS OF SCIENCE TEACHERS IN CANADA AND THE US
Our study follows several surveys conducted in Canada and the United States in the past decades that probed elementary, middle, and high school teachers about their practice of astronomy and science teaching: Krumenaker (2008Krumenaker ( , 2009aKrumenaker ( , 2009b; Plummer and Zahm (2010); Sadler (1992); Slater, Slater, and Olson (2009). We chose to concentrate on studies conducted in Canada and the US because of the similarities between school organizations in both countries, allowing valid comparisons between jurisdictions. To the best of our knowledge, no such study has ever been conducted in Québec. In this section, we will report major findings from two large surveys that are more closely aligned with our own and provide the best theoretical and practical basis for our research: Rowell and Ebbers (2004), and Banilower et al. (2013).
In their study, Rowell and Ebbers (2004) surveyed 1,116 elementary science teachers in Alberta, Canada, using a mailed paper-and-pencil questionnaire enquiring about several components of science teaching at the elementary level. Questions included demographics, the teachers' goals in teaching science, their background and experience, the resources and material they used, the abilities and interests of their students, and the support they received from their school.
The NSSME also discovered that elementary teachers teach science less longer and with longer intervals between lessons than other subjects, like reading/language arts and mathematics. Science is taught almost every day in only 20% of K-3 classrooms and in 35% of 4-6 classrooms, compared to 99% and 98% respectively for math. Many elementary students are taught science only a few days a week, or only during a few weeks during the school year. Science is taught on average only 19 minutes per day in grades K-3, and only 24 minutes per day in grades 4-6, compared to 89 and 83 minutes per day for reading/language arts respectively, and 54 and 61 minutes per day for math. The use of science specialists, either to replace or in addition to the regular classroom teacher, is infrequent in elementary schools.
The NSSME also found that the use of a science textbook or other reading material is more likely in elementary schools than in high school. Sixty-nine percent of elementary classes use textbooks in science, and teachers declare that they mostly use science textbooks to plan their teaching. Similar results about the use of textbooks in science teaching were found by Kesidou and Roseman (2002) and Hasni, Moreseli, Samson, and Owen (2009).
A majority of science teachers who completed the NSSME survey rated their resources in science as poor. The budget spent on instructional resources in science also seems inadequate, especially when evaluated as a per-student spending. The situation is especially grim in science in the elementary grades, where per-student expenditure is about half of that spent in middle schools and less than one-third of what is spent in high schools. Funds for purchasing equipment and supplies is also lacking in elementary schools. Teachers also complain about a lack of science facilities in the school, insufficient time to teach science in the class schedule, and poor or non-existent professional development opportunities in science for teachers.
The situation described above, based on Rowell and Ebbers (2004) and Banilower et al. (2013) results, is quite similar to the situation we find in Québec's elementary schools (see Chastenay, 2018). We now hope to be able to draw a clearer picture of the state of astronomy teaching in Québec's schools by constructing a logistic regression model based on the data collected by our survey instrument, described next.

SURVEY INSTRUMENT
Our original survey instrument is mostly based on Rowell and Ebbers' survey, which is itself based on the Science Council of Canada's National Study of Science Education (NSSE), conducted in the early 1980s (viz. Orpwood & Alam, 1984). One component of this vast study was a survey of elementary and secondary teachers addressing the following eight areas of interest in relation to science teaching: • General information (age, gender, years of experience); • Aims of science education (curriculum and instruction); • Teacher's background and experience (pre-and in-service); • Curriculum resources available/used (ministry guidelines, textbooks, etc.); • Physical facilities and equipment; • Institutional arrangements (time allocated to science teaching, teaching load, etc.); • Students abilities, profiles and interests; • Community and professional support.
Since the goal of our survey was similar to the Science Council of Canada's NSSE, we adapted and expanded these eight areas of interest (including the use of online resources, which was still futuristic in the 1980s) to create a 35question survey that probed several facets of teaching astronomy at the elementary level. Our questions touched upon the following aspects of astronomy teaching: Demographics (age, gender); teaching experience; pre-service education and training in science and technology; pre-teaching science and technology-related employment experience; astronomy and science teaching experience; number of hours per week of science teaching; demographics and socioeconomic information about the school, classroom, and students; perceived efficiency of pre-and in-service training in astronomy, in science and technology, and in science teaching; perceived need for in-service training in astronomy; and self-interest in teaching astronomy.
The survey questions were ordered along two major axes, one individual and the other temporal: questions went from the personal to the professional realms of a teacher's life, as well as from the past (before becoming a teacher), to the actual teacher's condition, and also to what would be desirable in terms of future experiences. Thus, the first items in the survey were more personal and looking back, targeting demographic issues, past formation, past experiences in science and in astronomy, then encompassed the actual professional situation of the teacher (class level and class type, number of students in the classroom, school's location, etc.). The next series of questions were a sub-set of the survey addressed specifically to elementary teachers that presently teach astronomy in their classroom: Integration of astronomy with other school topics (French, English, Math, etc.); astronomical topics taught; number of hours per year devoted to astronomy teaching; aims and goals of teaching astronomy; classroom arrangements, resources and equipment available; and perceived difficulties and obstacles to teaching astronomy. Finally, the last questions of the survey considered the teachers' training continuum from past to future, probing all respondents (astronomy as well as non-astronomy teachers) about their pre-service and in-service training, and their perceived need for future training in astronomy.
The initial version of the survey was first tested with several university colleagues (science education specialists) and six volunteer elementary teachers that do teach astronomy to their class, to ensure a high level of readability and understanding of the questions and suggested answers. The elementary teachers were also able to confirm that questions appropriately covered all aspects of their own daily experience of teaching science and astronomy in elementary classrooms, and made suggestions where needed. This version was then field-tested face-to-face with elementary teachers participating in a two-day professional meeting of the Association québécoise des enseignantes et des enseignants du primaire (AQEP), held December 12 and 13, 2013, in Québec City. Respondents were asked to answer questions by tapping their preferred answer on an iPod screen; the survey took about 10 minutes to complete and 138 elementary teachers completed it (see Chastenay, 2014, for preliminary results). The survey was then slightly modified in light of these results, and it became the online survey that we report upon in this paper (see Chastenay (2018) for a list of questions used in the online survey).
The online survey (in French only) was conducted from January to March, 2015. Invitations to participate were sent via several channels: direct emails, Facebook pages, professional newsletters, etc. Since invitations were sent in French only (the language spoken by the majority of the population in Québec), we do not believe that language was an issue in understanding the survey questions. A total of 701 individuals logged on the survey's welcome page and began answering questions, and 500 completed the 35 questions. We compared all IP addresses collected by the survey instrument (LimeSurvey) and found no duplicates, indicating that all respondents were probably unique visitors. It is worth noting that the majority of the 201 individuals who did not complete the survey answered "No" to question 15 ("Did you teach any astronomy topic to your class during the last school year?"), and went no further. Although the invitation messages and the survey's welcome page insisted that even elementary teachers who do not teach astronomy were firmly invited to complete the survey nonetheless, it seems that a lot of them chose not to go beyond the admission that they did not teach astronomy to their class. This anecdotal information leads us to believe that the fraction of elementary teachers in our survey who do not teach astronomy is probably underestimated (or, to say it differently, "Astronomy teachers" are probably over represented in our sample). Of course, since ours is a convenience sample, we cannot pretend that our results are a statistically perfect illustration of the situation of astronomy teaching in Québec's schools. Nonetheless, with 500 respondents, we can clearly see patterns and trends emerging from our results; we will describe and analyze them in the following section.

MAJOR RESULTS OF THE SURVEY
In this section, we briefly present the major results of our survey; see Chastenay (2018) for a more in-depth analysis of answers provided by elementary teachers. Our results show that the demographics of our sample is very similar to the general population of elementary school teachers in Québec (29,899 elementary teachers in 2014-2015), as described by Québec's Ministère de l'Éducation, de l'Enseignement supérieur et de la Recherche [MÉESR] demographic data (MÉESR, 2015): respondents are mostly female (91%), aged around 40 years old (M = 40.2 years, SD = 8.9), and cumulating about 16 years of experience teaching at the elementary level (M = 15.6, SD = 7.9). All respondents hold a four-year Bachelor's degree in Education, the minimum required in Québec to obtain a teaching license, but only 18% hold a higher degree (M.Ed. or Ph.D.). The schools where they teach, their socioeconomic status and geographical locations, the type of classroom, and their students' makeup, all are representative of Québec's typical elementary school, according to available census data (MÉESR, 2015).
Very few respondents to our survey have had a pre-teaching job experience in a science-related environment (8%); for those who did, it was mostly in science museums. Preferred science-related leisure activities are watching and listening to science TV and radio shows (76%), and visiting scientific web sites (55%). For most of our survey's respondents, the study of science, like physics, chemistry or biology, didn't go beyond high school. The vast majority of respondents teach science only about one hour per week (M = 1.2 hour, SD = 0.8), and 51% admit they don't teach astronomy at all in their classroom.
Respondents who said they teach astronomy to their class (49%) seem to cover the topics contained in Québec's elementary schools curriculum well, even though the majority of Astronomy teachers devote only about 10 hours per year to this subject (M = 10.3 hours, SD = 6.7). Their aims and goals in astronomy teaching are well aligned with Québec's school program objectives, which are to help students develop their competencies and learn core knowledge in astronomy. But astronomy teachers admit that they meet with a lot of difficulties when teaching astronomy: lack of resources and materials, old equipment of poor quality, lack of pre-and in-service training, inadequate classroom arrangement, not enough time in the class schedule, as well as their own feeling of being incompetent to teach the subject adequately.
A telling result is the choice of Internet (93%), trade books (70%), textbooks (53%), and other reading material like newspapers and magazines (38%) as the tools used by the majority of Astronomy teachers to teach astronomy. This tends to show that astronomy teaching in Québec's elementary schools is mostly done through reading and writing activities, a result that is congruent with similar findings by Hasni et al. (2009) concerning the teaching of science in Québec schools.
Pre-service training in astronomy was unavailable for the majority of respondents to this survey (59%); given the age group of the majority of elementary teachers who completed the survey (around 40 years old), most respondents had already completed their pre-service training well before astronomy was introduced in Québec's elementary school curriculum. What is more worrying is the very low level of satisfaction with pre-service training in science (59%) and in science teaching (55%). Also troubling is the fact that in-service training in astronomy is unavailable for 59% of respondents or, when available, seems to be mostly ineffective, even though the majority of respondents think they would need only a relatively short period of training time (M = 6.5 hours, SD = 5.2) to feel competent enough to teach the topic in class.
These last results might help explain why about 17% of all respondents surveyed admit they would rather not teach astronomy at all to their class, if given the choice. The reasons they provide are congruent with what we wrote previously about the difficulties of teaching astronomy in elementary school, like the absence or the poor quality of pre-service and in-service training, and also the fact that astronomy is not mandatory at the elementary level in Québec's schools. A lot of teachers admit they prefer to devote more class time to core subjects, like French and Math, which are incidentally the subject of two mandatory, province-wide Ministry of Education tests at the end of elementary school (cycle 3, grades 5 and 6). No such test exists in Québec's elementary schools for science and astronomy.
Since our survey sample contains an almost equal number of Astronomy (N = 244) and Non-astronomy (N = 256) teachers, it offers the opportunity to statistically compare answers from both groups to all questions in our survey, except questions 16 to 25 that were answered by Astronomy teachers only (see Chastenay, 2018). To make this comparison, we chose to build a logistic regression model that will reveal factors that are conducive or hinder the teaching of astronomy at the elementary level in Québec schools. We describe the details of the model construction in this section. Other statistical methods, like factor analysis or principal component analysis, were not favored for the simple reason that the survey was not constructed to be used with such approaches: each question in the survey was designed to measure a single dimension of astronomy teaching at the elementary level, hence there is very little correlation between variables that could lead to latent factors emerging from the data. Since our goal is basically to reveal factors that explain membership in one of two groups (Astro vs Non Astro), logistic regression is the method of choice.

Assumptions of Logistic Regression
Logistic regression is a form of regression that fits a model to data, based on one or several predictors (independent variables, categorical or continuous), to predict the outcome of a binary dependent variable (in the present case, to teach astronomy at the elementary level or not). Logistic regression is the method of choice when linear regression cannot be used because of the binary nature of the dependent variable (see Peng, Lee, and Ingersoll (2002) for a general discussion of the mathematical basis of logistic regression). That being said, logistic regression shares several assumptions with normal regression, namely: linearity between the outcome and the continuous predictor variables (although in the case of logistic regression, we use the natural logarithm, or logit, of the continuous variables); independence of errors (case data are not related, which is the case in this survey, since each respondent answered only once); and no multicollinearity is present (in other words, predictor variables are not too highly correlated) (Field, 2018). Also, data must be present for all combinations of the predictor variables (a condition known as complete information), and the outcome variable must not be perfectly predicted by one or a combination of predictors (i.e. complete separation). Before we create the logistic regression model, we will verify these assumptions in the following sections, using IBM's SPSS statistical software package (version 24.0).

Empty Cells
First, to check for empty cells, we produced multiway crosstabulations of all categorical independent variables (note that all continuous variables in our model have normal distributions and are thus not subject to this condition). We also verified that expected frequencies in each cell were greater than 1, and that no more than 20% of expected frequencies were less than 5, both necessary conditions to ensure the goodness-of-fit of the logistic regression model (Howell, 2006). Inability to meet these criteria may result in loss of statistical power. We report problematic variables below.
The variable Sex had to be rejected from the model because, in crosstabulations with other categorical variables, we found too many empty cells or cells with expected frequencies less than 1 (for example, with the variable Last Course in Physics & Chemistry). This is due to the fact that our sample is mainly composed of women (men represent only 9% of the sample). As we have seen previously, this is also true for the general population of Québec's elementary teachers (MÉLS, 2015). Other predictor variables that had to be rejected for the same reasons are Highest Diploma Obtained, Last Course in Math, School's ISEB 1 , School's Location, Science Specialist at School, and Preferred Moment for In-service Training in Astronomy.

Multicollinearity
Next, we checked for multicolinearity between predictor variables (except those rejected in the previous step). Since we have continuous as well as categorical variables, a recommended first step to explore colinearity between variables is to run a crude linear regression including all predictor variables (forced entry, see Field, 2018) and to look for Tolerance statistic values less than 0.1 (Menard, 1995) or values of the Variance Inflation Factor (VIF) statistic equal to or larger than 10 (Myers, 1990), both indicating potential problems of multicolinearity. We found Tolerance values between .317 and .930 (M = .679), and VIF values between 1.076 and 3.153 (M = 1.700). Consequently, there is no obvious sign of multicolinearity in our data at this point: the smallest Tolerance value is .317, well above .1, and the largest VIF value is 3.153, well below 10. What's more, the mean VIF is marginally larger than 1, which indicates that the regression is unbiased (Bowerman & O'Connell, 1990).
To complete the analysis, we also looked at variance proportions associated with the eigenvalues of each predictor. We are looking for predictors that have high proportions of their variance on the same small eigenvalue, indicating that the variances of their regression coefficients are somewhat dependent. In the case of our model, we find signs of colinearity between Age and Years of Teaching Experience in Elementary School; between Last Course in Physics and Chemistry and Last Course in Biology; and also between Last course in History and Last Course in Geography. We also find signs of colinearity between Satisfaction Toward Pre-service Training in Astronomy, Satisfaction Toward Pre-service Training in Science and Satisfaction Toward Pre-service Training in Science Teaching. To follow up on this colinearity analysis, we went a step further by calculating proper correlation coefficients between predictors that were previously identified as possibly collinear (Pearson's r between continuous variables and Cramer's V for categorical data). Table 1 presents the results.  Table 1 quantitatively confirms the results of the exploratory linear regression for collinearity conducted before. Results show that there is a strong, positive correlation (larger than .5, see Cohen, 1988) between Age and Years of Teaching Experience in Elementary School (obviously, these two predictors evolve at the same rate and are clearly related), as well as between Satisfaction Toward Pre-service Training in Science and Satisfaction Toward Pre-service Training in Science Teaching (two subjects often taught together in Québec's teachers preparatory schools, sometimes in the same course). Correlation is moderate and positive between Satisfaction Toward Pre-service Training in Astronomy and both Satisfaction Toward Pre-service Training in Science and Satisfaction Toward Pre-service Training in Science Teaching. Finally, there is moderate and positive correlation between Last Course in Physics & Chemistry and Last Course in Biology (these courses are often taken together by high school students enrolled in a science program), and strong correlation between Last Course in History and Last Course in Geography (again, these courses are often taken together by students enrolled in a humanities program).
Because these correlations might add too much colinearity to our model, it is best to reject one of each correlated variables; otherwise we will not meet an important assumption of logistic regression. Since collinear and correlated variables are essentially redundant in our model, having the same effect on the outcome variable (all correlations are positive), we can safely proceed by keeping only one of each (Field, 2018). In our logistic regression model, we will thus keep the independent variable Years of Teaching Experience in Primary School instead of Age, since it is a more representative factor than age to assess a teacher's experience. We will also retain Last Course in Physics & Chemistry instead of Last Course in Biology, since physics is more closely related to astronomy than biology, and Last Course in History instead of Last Course in Geography, since history, in contrast to the natural sciences, is more representative of studying the humanities than geography is. We will also retain Satisfaction Toward Pre-service Training in Science Teaching instead of Satisfaction Toward Pre-service Training in Science (the former having a slightly smaller correlation factor with Satisfaction Toward Pre-service Training in Astronomy than the latter). But we definitely want to keep the variable Satisfaction Toward Pre-service Training in Astronomy, even though there's a moderate correlation with Satisfaction Toward Pre-service Training in Science Teaching, since it will very likely be a central variable of our model. At the end of the process, we will be able to test for residuals and see if there remains too much multicolinearity in our model because of this inclusion.

Linearity
Finally, we verified that the outcome binary variable Astro vs Non Astro had a linear relationship with the natural logarithm of the continuous predictor variables that were not rejected in the previous steps. indicating that the assumption of linearity of the natural logarithm of these variables with the binary dependent variable has been met for all continuous variables in the model.

Choosing the Independent Variables in the Model
The next question we need to answer before proceeding with the logistic regression is whether all the remaining variables have their place in the model or not, since we wish to be able to determine with the greatest accuracy possible, but also with the most parsimonious model, the odds that, given an elementary teacher's answers to the questions associated with these variables, he or she will opt to teach astronomy in his or her classroom or not. To answer this question, we must now turn to theory and previous research on the teaching of astronomy in elementary schools. As we have stated before, this is the first study of its kind to be conducted in Québec, so there is no previous research in the province for us to base our reflection upon. We briefly presented in the introduction of this paper two important studies conducted in Alberta and in the United States whose conclusions will help us to choose the most promising variables to build our model. Table 2 briefly presents the justifications for the inclusion or rejection of each remaining predictor variable. Teachers more familiar with science teaching and doing more science in their classrooms every week might also teach more astronomy Satisfaction Toward Preservice Training in Astronomy + Teachers having received more satisfactory pre-service training in astronomy might teach more astronomy in their classrooms Satisfaction Toward Preservice Training in Science Teaching + Teachers having received more satisfactory pre-service training in science teaching might teach more astronomy in their classrooms Previous Science Job + Teachers having more experience with science in the context of pre-teaching employment might teach more astronomy in their classroom Participation in Science Leisure Activity + Teachers participating in more science leisure activities might teach more astronomy in their classroom Participation in In-service Training in Astronomy + Teachers participating in more in-service training in astronomy might teach more astronomy in their classroom Number of Hours of Inservice Training Needed − Teachers feeling that they need longer in-service training in astronomy might teach less astronomy in their classroom Efficacy of In-service Training in Astronomy + Teachers feeling that they received efficient in-service training in astronomy might teach more astronomy in their classroom Prefer not to Teach Astronomy − Teachers preferring not to teach astronomy in their classroom might in fact teach less astronomy In summary, after removing variables that do not comply with the complete information assumption, and those that are too strongly correlated, after checking that there is indeed a linear relationship between the binary dependent variable and the natural logarithm of the continuous independent variables, and finally choosing among the remaining variables which ones will be retained in the model, we are left with 15 predictor variables (see Table 2), each associated with a single question of the survey of Québec's elementary teachers, to build our logistic regression model. Hosmer and Lemeshow (1989) and Cohen (1992) suggest that the minimum sample size for a logistic regression should be 10 times the number of predictors, which amounts to 150 in our case. Since our sample is N = 500, that places us well above the minimum threshold recommended. We can thus proceed with the logistic regression. Table 3 presents the complete logistic regression model (forced entry). It allows us to correctly classify 74.9% of teachers in our sample, with a significance level given by a Pseudo R 2 of .273. This last figure is an estimate of the level of improvement from the null model to the best-fit model presented in table 3 or, in other words, the ratio of what the model can explain compared to what there was to explain at the beginning. The final model therefore predicts 27.3% of the variance of the probability of teaching astronomy at the elementary level in Québec's schools. Also, the Hosmer and Lemeshow goodness-of-fit statistic for the model, including nine independent variables, is not significant (c 2 (8) = 11.984, p = .152), leading us to retain the null hypothesis that the model is a good fit to the data. Finally, testing for residuals, we want to make sure that the standardized residuals follow a normal distribution without too many outliers (Field, 2018). We find only six values whose standardized residuals are located outside the range ± 1.96 containing 95% of the distribution of scores (1.2% of the total sample), three of which have standardized residuals outside the range ± 2.58 containing 99% of the distribution of scores (0.6% of the sample). Since these percentages of 1.2% and 0.6% are well below 5% and 1%, respectively, and no standardized residual is found outside the range ± 3.29, all assumptions of a normal distribution are met, and we can safely claim that the logistic regression model is well adjusted to the data and effectively tells, based on answers to the survey questions related to the nine variables included in the model, which elementary teachers belong to the Astronomy and Non-astronomy groups, respectively. The significance level of the Wald statistic (noted with one to three asterisms after the value of B in Table 3) indicates which predictor variables do have a significant effect on the outcome (i.e. their regression coefficient is significantly different from zero) and those who don't. One can also see that predictor variables whose contribution is not significant have a 95% confidence interval for the odds ratio exp(B) that crosses the value of 1. It is also consistent with our initial predictions (see Table 2) that teachers already teaching more science in their classroom will teach more astronomy, and that the few who have received pre-service training in astronomy, and were satisfied with it, will teach more astronomical topics in their classroom.

The Logistic Regression Model
Finally, we find that teachers who participated in in-service training in astronomy, and teachers that were satisfied with this in-service training, are more likely to teach astronomy to their students. This is exactly what was expected when we introduced these two variables in the model. We also predicted that teachers who declare that they would need more hours of in-service training in astronomy to feel comfortable teaching this topic, as well as those who would rather not teach astronomy, would be less likely to teach this topic to their students. These two variables might illustrate a lack of confidence or feeling of incompetence on the part of the teachers toward astronomy teaching.
Among the variables that do not contribute significantly to the model, we were surprised to find that the four that had to do with previous training and general interest in science (Last Course in Physics, Satisfaction Toward Pre-service Training in Science Teaching, Previous Science Job, and Participation in Science Leisure Activity) did not influence the model. This goes to show that, contrary to our expectations (also voiced by Rowell and Ebbers (2004) and Banilower et al., 2013), a solid background in science and in science teaching before becoming a teacher does not seem to be an essential prerequisite to teach astronomy at the elementary level. By the same logic, Last Course in History, representing a formation in the humanities instead of natural sciences, do not seem to hinder astronomy teaching either.
Finally, in the case of Years of Teaching Experience in Elementary School, our initial prediction was that it could have been either conducive to astronomy teaching or not, depending on the interplay between having more years of experience, but no pre-service training in astronomy (because training was completed before the introduction of astronomy in the curriculum), or less experience, but with pre-service training in astronomy (as the teachers prep schools adapted to the new curriculum since astronomy was introduced). The lack of significance of the result in the logistic regression model may indicate that antagonistic tendencies between years of teaching experience and having received pre-service training in astronomy or not are present in our data and cancel each other out. To check if such is the case, we ran a second logistic regression with the same variables as previously described (Table 3), but added a new one representing the interaction between Years of Teaching Experience in Elementary School and Satisfaction Toward Pre-service Training in Astronomy, on the basis that this interaction might help sort out contributions by both. Unfortunately, this new variable was not contributing significantly to the model (p = .117) and had to be rejected.
What can we make of these results in terms of suggestions that might positively influence the decision by elementary teachers to actually teach astronomy in their class? We think that if we view the variables that contribute significantly to the logistic regression model as factors that may facilitate or hinder astronomy teaching at the elementary level in Québec schools, we can make the following propositions (numbers in square brackets refer to the associated predictor variable in the logistic regression model, see Table 3): • Offer high-quality pre-service training in astronomy to future elementary teachers [5]; • Offer high-quality in-service training in astronomy to actual elementary teachers, with a duration appropriate for their needs [6, 7, 8]; • Raise the profile of science teaching (and astronomy teaching) in elementary schools, specifically targeting teachers that teach less science in their classroom or would prefer not to teach astronomy in class [4,9]; • Remind teachers in kindergarten and grades 5 and 6 of the importance of astronomy teaching and covering the standards contained in the curriculum for their school level (a province-wide, Ministry of Education exam in science at the end of elementary school might go a long way in attaining that goal) [1]; and • Help elementary teachers with poor, immigrant and disabled students, and part-time teachers, to realize that astronomy teaching offers many possibilities to raise the level of interest of their students, make connections with other school topics (language, math, etc.) and render school more relevant to them [2, 3].
To sum up, it follows from our results that the promotion of astronomy teaching at the elementary level should be done through effective pre-service as well as in-service training in astronomy and in science. This conclusion is similar to what Rowell and Ebbers (2004) and Banilower et al. (2013) reported in their respective studies. For example, writing about the effectiveness of in-service training and comparing with results from the 1984 study by Orpwood and Alam, Rowell and Ebbers note that "elementary teachers' perceptions of the effectiveness of in-service programs for school science in their schools or school districts have changed very little over the past 20 years; many teachers suggest that it is ineffective." (2004, p. 62) The authors were also concerned that very few teachers have studied science at the university level (pre-service training), and suggest that in-service programs with duration between 5 and 20 hours per year should address contemporary science to bridge that gap.
In their report, Banilower et al. (2013) state that one of the main factors perceived by a majority of school teachers as promoting effective science instruction at the elementary level is their school and school district's science professional development (PD) policies and practices; time devoted to PD is also seen by teachers as one of the best way to promote science instruction in their classroom. Several science program representatives in elementary schools view inadequate science-related PD opportunities as a serious problem inhibiting science instruction.
Banilower et al. also remark: "it is somewhat surprising that in science, only about half of schools are in districts that organize professional development based on the standards.
[This] raises the question of how work to align instruction with standards is being done, if not in professional development." (2013, p. 113) What kind of PD works best? Again, Banilower et al. suggest that "professional development workshops and teacher study groups can provide important opportunities for teachers to deepen their content and pedagogical content knowledge, and to develop skill in using that knowledge for key tasks of teaching, such as analyzing student work to determine what a student does and does not understand. When resources allow, going the next step and offering one-on-one coaching to help teachers improve their practice can be a powerful tool." (2013, p. 47) We believe that promoting such measures will indeed give elementary teachers the tools and confidence they need to efficiently teach astronomy to their students, and that this will ultimately lead to better astronomy teaching in elementary classrooms across Québec. We also believe that the same measures could be promoted in other jurisdiction (provinces or states) in which astronomy teaching at the elementary level is lacking.
If the measures we are proposing are indeed implemented, it would be interesting and useful to repeat the survey in 5 to 10 years from now, to measure their impact. Also, since the introduction of astronomy in Québec's school curriculum in the mid-2000s, pre-service training programs offered by different universities across the province have been modified to include astronomy; a repeat of the survey in about 10 years will allow us to measure the effectiveness of these new pre-service programs on the population of Québec's elementary teachers.