By Traci Kutaka
As any Primarily Math teacher will tell you, the purpose for a career in elementary education is all about the students. The Child-Belief survey was developed to learn how young students view themselves as learners of mathematics. What we learned from the results may surprise you.
It's likely that you recall the five questions from the Primarily Math Child Belief Pictorial Survey:
1. How good are you at math?
2. How good are you at math compared to your classmates?
3. How good are you at math compared to your other school subjects?
4. How well do you expect to do in math this year?
5. How good would you be at learning something new in math?
Although the questions seem rather straightforward, there is actually a lot that goes into designing such a survey. For example, this survey was constructed as a collaborative effort between four departments at UNL: Child, Youth and Family Studies; Psychology; Mathematics; and Teaching, Learning and Teacher Education.
But just writing a list of questions is not enough. In order to assess the validity and reliability of the survey (i.e. does it measure what we say it measures), we interviewed 120 students (30 per grade level) and asked them to define math with questions like: Have you heard the word "math" before? When do you have math time? What do you do during math? Do you ever see or do math outside of school?
So why go through all of this trouble? Why should we be concerned with "Child Beliefs" regarding learning mathematics?
Generally speaking, self-beliefs do matter in learning mathematics. Psychologist Arthur Combs stated, "Perhaps the single most important cause of a person's success or failure educationally has to do with the question of what he or she believes about themselves."
Developing conceptual understanding is necessary, but
by itself does not guarantee a student will acquire mathematical proficiency; there is evidence that feelings and emotions, which underlie motivational dispositions for learning, effect mathematical performance and skill development.
What have we learned as a result of developing and administering this survey?
Not only did we learn about students, we also learned something about the survey itself. This is the first instrument we know of that was designed to measure "healthy beliefs about the self as a learner of mathematics." Since this is one of the five strands of a productive learning disposition, it's an important characteristic to measure. Thanks to the child interviews and other statistical data collected, the survey was found to be a valid and reliable instrument (more so for older than younger students) for measuring beliefs related to learning mathematics.
What did we learn from the survey about children?
Results from the survey showed us some of the differences and similarities in responses among grade levels. For example, kindergarten and first grade students were more likely to rate themselves as good at math compared to their older peers (this was not a novel finding). What was surprising, however, was that at each grade level, 12 percent to 15 percent of students reported that they were poor at math. And, that boys and girls were equally likely to evaluate themselves to be poor at math.
Perhaps most interesting are the reasons (as revealed in interviews) students believe themselves to be good at math. In the younger grades, students talked about the role of effort (e.g., "I sit there nicely with my brain and think of numbers hard."). Older students believed that being good at math meant they did not have to struggle to complete teacher-appointed tasks (e.g., "It was easy to finish the worksheet.") or that they typically get a significant number of answers correct (often with no mention of how many they got incorrect; e.g., "I get answers right.").
In contrast, two reasons students believed themselves to be poor at math were because they got a significant proportion of answers incorrect, or because they were slower in completing math games or tasks relative to their classmates.
So what might teachers take from all of this?
It is important to keep in mind that positive, healthy self-competence beliefs do not guarantee that learning will occur, but negative self-competence beliefs do put young children at risk for academic disengagement. Moreover, teachers are in a position to understand and then act on students’ beliefs as their students construct identities as learners. For example, you may find that a student believes the speed at which he or she completes a task is equivalent to being "good" at math. Knowing this can help you respond to this student in ways which acknowledge the values of, say, working hard, or coming up with creative strategies. A teacher might also consider whether there something in his or her classroom environment that is communicating an unintended message about what it means to be "good" at math.
On a personal note: I would like to thank all of the teachers for administering this survey. Your accommodations made it possible for me to begin to better understand productive mathematical learning dispositions as well as complete my dissertation work. I am currently working on a manuscript to publish my findings in an academic journal and other journals that speak directly to teachers.
- Traci Kutaka, Ph.D., Psychology