Research Question 2: What are mathematics teacher beliefs about the purpose of assessment and feedback?
Assessment beliefs. As the participants responded to interview questions that
probed their perceptions and beliefs about assessment, a shared belief among all three participants was that the purpose of assessment was to check for understanding of the level of student learning of the curricular content. Teacher 1 said that assessments were “to show where they are, their level of understanding.” Teacher 2 stated that assignments were given in order to “gauge if the students are learning” and to “gauge that they got the concept down.” Teacher 3 expressed that the assessments were “to make sure that kids are mastering the concepts they need to take steps forward” and to “make sure that they understand the steps.” The assessments shared by the participants corroborated this belief
and were aligned with the lesson topic to see if student understood the concepts that were taught by the teacher.
Additionally, the syllabi for Teacher 2 stated that students “are checked for
understanding through dialogue and guided practice problems.” While only the syllabi for Teacher 2 had data that related to checking for understanding, the practice of checking for understanding was evident during the classroom observation of all three teachers in the form of teacher questioning and reviewing of practice problems.
All three teachers expressed through interview data their assessment beliefs included the stance that students should have the opportunity for multiple or repeated attempts. However, the implementation of this belief into their teaching practice differed. Teacher 1 would let “lower level students” redo daily work, but not allow it on quizzes or tests. Teacher 2 stated, “if they don’t get it the first time, well, then try again. Don’t get it the second time? We’re going to try it again.” Teacher 2 expressed the strategy of using multiple attempts for students earlier in the learning process prior to a more significant assessment rather than redoing the assessment and mentioned being “strict as in a sense of we are going to keep at this until we get it right.” Teacher 3 preferred to “give the kids as many opportunities to show me that have the stuff down” and stated that opportunities are offered outside of class to redo any problems students got wrong and to take a
secondary test. Teacher 2 credited being a parent as an influencing factor in giving repeated attempts to students, while Teacher 3’s belief stemmed from having lower level students who “struggle a bit more in math so I think I need to give them opportunities.”
Feedback beliefs. From interview data, all three teacher participants
communicated their beliefs regarding the importance of feedback. According to Teacher 1, feedback should clarify students’ understanding with the purpose of guiding and modeling correct mathematics procedures. Additionally, Teacher 1 expressed using feedback to help students find their own mistakes, stating “I try not to solve the whole problem for them but maybe circling or underlining or sometimes I write a sentence or a question or a leading question like—‘What would you do if you do this?’” Teacher 1 described good feedback as “giving a student a chance to think about where their error is” and poor feedback as information that is “inconsistent, inaccurate”, “meaningless”, or “if it made them feel awful about themselves.” The feedback information provided by Teacher 1 was typically knowledge of results in the form of the number wrong or correct and the resulting letter grade or percentage and it was stated that the teacher attempted to return corrected work by the next day.
Teacher 2 defined feedback as “giving information as to where the student stands so that they know how they are doing” and whether they have succeeded or not. Teacher 2 explained that the purpose of feedback “certainly can be motivating—if it’s positive” and described good feedback as “detailed, so that it’s not just ‘good job’; it’s why it is a good job.” Poor feedback was characterized as “doing a poor job because it’s just unmotivating and is not going to help them along the way. I think it can be poor also if it’s given— you know— tritely, if you just complement everything that happens.” The timing of feedback could be immediate as would happen during a lesson, or daily in the
form of returned student work. The type of information that Teacher 2 described as given to student was about the method in the mathematical process.
Showing students what they did wrong and how to perform the correct
mathematical steps are “unbelievably valuable” and “super important” uses of feedback whether it comes from a teacher or another student, according to Teacher 3. Good feedback “comes from not so good work” in order to “show the correct way to do it,” while feedback can be poor when a student doesn’t know what it means. Teacher 3 described the importance of giving the lower-level students feedback daily in the form of corrected work and a grade while also taking time to give student individual verbal feedback during a class period.