1. A Survey of Teachers’ Beliefs about Statistics and their Relationship to Teachers’ Resources
Travis Weiland
Kaput Center – School of Education
Abstract
Methods
Table 3
Difference in teachers with and without statistics teaching experience means beliefs scale scores.
Bootstrapped
Levene's Test
Independent Samples
t-test
95% CI Fa tb
Mean Diff.
Low
Upp.
SE Scale Avg
.85
5.56***
.756
.5799
1.2290
Value Scale Avg
2.24
3.65***
.331
.2215
.7554
Value Stu. Scale Avg
1.06
3.90***
.541
.3050
.9450
Curric. Scale Avg
.67
1.89
.393
-.0209
.7917
Total Scale Avg
.70
4.91***
.545
.3941
.9341
Note. ***=p≤.001, adf=(1,70), bdf=70
This study surveyed high school teachers’ beliefs toward the concepts described in the statistics content strand of the CCSSM (NGA Center & CCSO, 2010) and their resources, as well as possible relationships between their beliefs and their resources. Four belief elements were studied teachers’ self-efficacy beliefs for teaching statistics concepts, value of statistics in everyday life, value of statistics for students, and place of statistics in the curriculum. Correlational analysis was used to look at the possible relationships between the belief elements and teachers’ resources. Findings include that teachers’ belief about the value of statistics seems to be a central belief of those studied, and teachers’ previous experiences teaching statistics has a significant association with teacher’s beliefs
Participants
Participants were selected for this study by selecting school systems from various settings, in states from different regions of the country that are implementing the CCSSM (NGA Center & CCSO, 2010). 997 High school mathematics teachers from these selected schools that had publically available addresses on their school’s web site were then contacted to participate in the study; 72 agreed to participate. The teachers that responded to the study had an average of years of teaching experience ranging from 1 to 37 years. Of the respondents, 24 had previous teaching experience with statistics with an average of 6.5 years ranging from 1 to 25 years.
Table 2. Teachers’ resources surveyed
Number of college mathematics courses each teacher had taken
Number of years teaching
Number of years teaching statistics
Level of exposure to statistics during:
High school
College
Professional development levels.
Level of familiarity with standards documents including:
The Principles and Standards for School Mathematics (NCTM, 2000)
CCSSM ( NGA Center & CCSO, 2010)
Guidelines for Assessment and Instruction of Statistics Education (Franklin et al., 2007)
State Standards
Quality of text used
Amount of the text covered
Percentage of text containing statistics concepts
Availably of statistical analysis software such as SPSS or Fathom
Framework
Conclusions
Beliefs are an important aspect to consider in predicting the behaviors of teachers in the classroom (Pajares, 1992; Schoenfeld, 2011; Speer, 2005; Thompson, 1984, 1992). Teachers’ professed beliefs have been found to have significant connections to their observed classroom practices (Cross, 2009; Wilkins, 2008), and to act as a mediating variable between content knowledge and classroom practices (Wilkins, 2008). Furthermore, teachers’ beliefs have been found to change from subject to subject or context to context (Beswick, 2005; Cross, 2009).
For this study, I have adopted Törner’s (2002) four component structural framework to guide the understanding of beliefs (Goldin, Rosken, & Törner, 2009).
The first component of beliefs is that they have a belief object (O).
The second component is the content set associated with the belief object, as beliefs themselves consist of a wide array of mental constructs such as ideologies, attitudes, or perceptions.
The third component is that the elements of the content set have varying degrees of membership in terms of levels of certitude, consciousness, and activation, which change with the context in which they are situated (Törner, 2002).
The fourth and final component is an evaluation measure, in that beliefs are intertwined with emotional feelings and values that express a level emotional approval or disapproval, favor or disfavor associated with beliefs (Goldin et al., 2009).
The findings suggest that the belief elements of teachers’ self-efficacy towards teaching statistics, value for statistics in everyday life, value of statistics for students, and the place of curriculum in the high school curriculum are separate but significantly associated.
The value for students’ belief element appears to be a central element of the content set of the belief object for teachers’ beliefs about the statistics concepts in the statistics strand of the CCSSM (NGA Center & CCSO, 2010).
The single greatest resource that influenced these teachers’ beliefs was whether or not they have previous experience teaching statistics shown in Table 3.
The relationship between the quality of teachers’ text, amount of the text covered and teachers’ self-efficacy beliefs in teachers with previous experience teaching statistics implies that there is a significant relationship between teachers’ curriculum and their beliefs about their ability to teach statistics effectively. This relationship needs to be further investigated as it could have significant implications for the type of curriculums that should be used in teaching statistics.
One relationship that could have serious implications for the incorporation of statistics concepts into the high school curriculum is the significant negative association between the rank of the statistics strand in the CCSSM (NGA Center & CCSO, 2010) and the teachers’ belief elements scale averages.
Also a disturbing negative relationship was found between the number of years a teacher has been teaching and their belief elements scale averages, which implies that teachers’ belief element scale averages decrease the more experience they have teaching with no experience teaching statistics. Unfortunately this pattern has been found in other studies as well (Estrada & Batanero, 2008).
Data Source
The data for this paper was collected using a survey comprised of a mixture of multiple-choice, ranking, Likert scale (1-5) and open-response items. The Likert scale items were designed to assess the four belief components drawn from previous studies or created as described in Table 1. The ranking items had teachers rank the content strands and the main statistics topics of the CCSSM (NGA Center & CCSO, 2010) in terms of importance for students to learn. The multiple-choice and open-response items were designed to provide categorical or quantitative data on teachers’ resources (Table 2) to allow for a statistical analysis.
Data Analysis
 The data was analyzed quantitatively using correlational analysis (Field, 2013), to investigate possible relationships between the scale scores for the teachers’ belief object elements and the teachers’ resource. Pearson’ correlation coefficients were used for continuous data and Spearman’s rho coefficients were used for discrete and categorical data.
Table 1. Teacher belief scales
Scale
# Items
Purpose
Self-Efficacy for Teaching Statistics (SE) 12
Survey was originally created to measure elementary school teachers self-efficacy beliefs about teaching mathematics (Enochs, Smith, & Huinker, 2000). Modified to measure mathematics teachers’ self-efficacy beliefs for teaching statistics.
Value of Statistics (V) 9
Originally created to measure college statistics students’ value of statistics in the workplace and everyday life (Gal, Ginsburg, & Schau, 1997).
Value of Statistics for Students (VS) 5
Created to measure teachers’ degree of agreement on the value of statistics for their students focusing on the value of statistics for students in their everyday lives, as well as for college.
Place of Statistics in the Curriculum (PSC) 4
Created to measure teachers’ degree of agreement with the placement of statistics concepts in the high school curriculum.
Findings
Table 8. Spearman’s rank correlations for belief scale averages and resources for teachers who have never taught statistics. Only resources with statistically significant correlation to beliefs shown
Self-Efficacy Scale Avg
Value Scale Avg
Value for Students Scale Avg
Curriculum Scale Avg
Total Scale Avg
# Years Teaching
-.370**
-.291*
-.383**
-.202
-.368*
CCSSM Fam.
.196
.330*
.251
.311*
.312*
High School
.470**
.066
.084
.273
.324*
College
.384**
.320*
.271
.195
.346* PD
.322*
.056
.225
.255
.305*
Stats & Prob
-.417**
-.508**
-.325*
-.422**
-.505**
CCSSM 5
-.330*
-.197
-.293*
-.300*
-.333*
% text stats
.361*
.269
.278
.303*
.357*
Note. *=p<.05, **=p<.01
Table 7. Spearman’s rank correlations for belief scale averages and resources for teachers who have taught statistics. Only resources with statistically significant correlation to beliefs shown
Self-Efficacy Scale Avg
Value Scale Avg
Value for Students Scale Avg
Curriculum Scale Avg
Total Scale Avg
# year teaching stats
.739**
.463*
.401
.247
.638**
NCTM Fam.
.213
.058
.278
.437*
.216 PD
.621**
.509*
.384
.326
.557**
Functions
.293
.454*
.177
.072
.358
Geometry
-.416*
-.006
-.229
-.108
-.312
Stats and Prob
-.489*
-.499*
-.358
-.196
-.488*
Text quality
.470*
.335
.315
.174
.440*
% text covered
.597**
.503*
.391
.274
.544**
Note. *=p<.05, **=p<.01
Limitations
Table 4. Partial correlations coefficients [percentile bootstrapped 95% CIs] for each pairing of belief element scale score averages controlling for the other belief element scale score averages.
Scale Averages
Value
Value for Students
Curriculum
Self-Efficacy
.126 [-.160, .431]
.346** [.014, .578]
.014 [-.210, .233]
.548*** [.406, .686]
.071 [-.176, .293]
.521** [.348, .670]
Note. **=p<.01, ***=p<.001
There are limitations to this study the biggest being that the survey instrument used to collect all of the data has not been validated. Another limitation is that the sample was not a true random sample which prevents from any generalizations being made beyond the sample.