ENACTMENT OF AND RATIONALE FOR USING FORMATIVE ASSESSMENT STRATEGIES
7.3 Teacher educators’ implementation of formative assessment
7.3.1 Questioning as a formative assessment strategy
Black and Wiliam (1998a) observed that when teachers use assessment formatively, they should apply a questioning strategy as an opportunity to improve and enhance students' knowledge.
During the interview, all participants acknowledged the importance of questioning in their instructions. Classroom observation revealed that questioning was the most dominant informal FA strategy teachers employed in their instruction. Although all teacher educators used questioning during their instruction, implementation of this strategy differed across the individual participants. Questions were used at various instruction stages: at the beginning of instruction, during instruction, and at times in the instruction's closing stage. Based on the lecture observations, teacher educators spent a few minutes at the beginning of each lesson giving a general review of the previous meeting. For example, at the start of his lectures, Sekyi reviewed the previous lesson by summarising the concept discussed in his previous encounter with the students. He followed this up with questions for the students to attempt to answer. This is exemplified in the excerpt quoted from his lesson below:
The last time we met, we discussed the various ways in which we can factorise or find the solution or the zeros of a quadratic equation. First, we discussed the factorisation method and as we went further one of us drew our attention to the fact that there is a limitation, especially with the factorisation approach. We observed that with the factorisation approach, we find the factors by multiplying the coefficient of 𝑥2 [a] by the constant [c] in the equation to obtain [ac]. Then find two numbers, which are factors of ac and when multiply gives the product [ac], and when added, gives the coefficient of 𝑥 [b]. But we saw that in some of the equations, it is not possible to factorise. Another approach that we consider very useful was the completing of squares, but unfortunately, we could not finish. I want us to
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go through with this approach. For instance: find the zeros for the equation 𝑥2+ 5𝑥 + 2 = 0, using the method of completing squares.
In the extract above, Sekyi reminded students about the previous lessons instead of posing questions to elicit responses. Although he made an effort in checking students' understanding of the quadratic equation by giving them questions to try on their own, his method has some limitations as the focus was on the answer, not the explanation. In the last sentence he is instructing students to use a particular approach rather than allowing them to use their own approaches. The literature postulates that teachers’ implementation of FA in the classroom should aim to enhance students’ learning, and using questions and answers is one of the strategies to achieve that. While Sekyi claimed to be using questions and answers as an assessment strategy in the interviews presented in Chapter 5, the above extract seems to suggest that he is not – because instead of using questions and answers to elicit responses from students to inform the learning of the new lesson, he was recapping for the students.
The other five teacher educators did use questions and answers to elicit students' understanding.
For example, Anani used questions and answers as a baseline assessment to understand students' existing knowledge or what students know about the yet to be discussed concepts. The following were questions he posed with the intention of finding out what the students know before introducing his lesson:
“What do we mean by statistics? What is statistics?” [Repeating and Rephrasing]
“What is data when we are doing statistics?”
“What is discrete and continuous data?”
In another example, Emily asked the following set of questions orally before introducing her students to the topic of integers:
“Who is owing someone money?”
“How much do you owe her?”
“How much were you having before she borrowed the 5. 00 cedis?”
“How are we going to write this 5.00 cedis she owes mathematically?”
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Jiang (2014) argued that it would be inapposite to label questioning aimed at diagnosing learning as an FA strategy if follow-up actions are not taken to facilitate learning. Drawing from the preceding excerpts from the lesson observation transcripts, it is evident that Anani and Emily adopted questioning formatively, in line with the claim advanced by Jiang (2014). It can be argued that the follow-up questions posed by the two educators (Anani and Emily) were to enable them to find out what the students know about the topic, to identify gaps in the students’ knowledge and understanding, and to scaffold the development of the students’ understanding in order to close the gap between what the students know currently and the learning goals. Although these teacher educators utilised questions formatively, the questions asked were low-order questions that do not challenge students' thinking, but rather gather information needed to establish what students know.
These kinds of questions, according to Feng (2014), require students to recall facts or definitions and can be situated under the knowledge, comprehension, and application levels of Bloom's taxonomy in accordance with Bloom’s continuum for categorising questions.
In other scenarios teacher educators developed reasoning and structural questions to generate data on how students think. Reasoning and structural questions provide rich information to understand students’ thinking, as evident in the following two classroom observation transcripts:
Fordjour asked the students to solve the triangle with sides 6, 14, and 16 units. He asked "What is the question looking for specifically?” One student answered that they thought they were to calculate the angles. Fordjour responded “How do we go about it?” and the student replied “Bec- ause we are to calculate the angles, we have to first draw a right-angle triangle, then calculate the angles using the trigonometric ratio.” Fordjour asked the class whether the student was correct.
The class responded “No, Sir”, and Fordjour repeated the question by asking the students “How can this be solved?” Another student then replied “I think one needs to use the concept of Pythagoras triple to establish if the numbers 6, 14, and 16 form the sides of the right-angle triangle before the triangle can be considered as right-angle triangle.” Fordjour then asked the students to use the Pythagoras triple to check if 6, 14, and 16 form the sides of a right-angle triangle.
Peprah asked her students to determine the amount that a government worker shared between his two children, Isaac and Rose, in the ratio 4: 5, if Isaac’s share is Ghc 15 000. She then asked “What
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is the total quantity shared?” and some students replied “9”. Peprah confirmed that 9 represents the quantity or the total amount shared. She then walked around the lecture room and observed as the students worked on the activity. She went on to ask “The 4th part has been given as Ghc 15 000; what amount will determine the 5th part?” A female student replied “Rose's share, which is the 5th part, is Ghc 18 750”. Peprah quizzed the student: “How did you get that?” The student replied “If Isaac's share is Ghc 15 000, then Rose’s share is 𝑥. So, this in ratio gives 15 000: 𝑥 = 4:5, then you solve for 𝑥, which is 𝑥 = (15 000 × 5) ÷ 4 = Ghc18 750.” Peprah then asked
“What then is the total amount shared?”. The students replied, “Total amount shared is Ghc 33 750”. The students were actively involved in the process.
The preceding excerpts from the lesson observation transcripts delineate the FA practices of Fordjour and Peprah, and present evidence of teacher-student interaction in the teaching and learning process in which the teacher produces and acts on students’ response. Bekoe, Eshun, and Bordoh (2013) remarked that interactive FA promotes learning outcomes through questioning in the form of dialogue. Unlike Anani and Emily's use of questions and answers, in Fordjour and Peprah lessons the students were empowered to argue and justify their ideas; based on that, teacher educators recognise and take into account a range of students' ideas to gain a clear picture of students’ understanding (Ruiz-Primo, 2011).
In the same manner, Wilson elicited his students' knowledge and understanding of investigating number patterns, specifically generating a 4 x 4 magic square using the numbers 5, 6, 7,8 … 20,
and made instructional moves to assist them in advancing their learning.
Furthermore, classroom observation revealed that students’ questions played a critical role in the learning process and were envisioned as a resource for the teaching and learning of mathematics.
That is, teacher educators recognised the students' questions in the assessment process during teacher-student interaction on mathematics content in the classroom. Students had the opportunity to ask questions to clarify concepts and for a deeper understanding, as evident in the excerpt below:
Sir, the other time you said with Cuisenaire rod, you can use two rods as a whole, but the explanation was not clear. You said you could use say yellow and red rods as a whole.
Could you please explain further and give additional examples?
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The student’s question was purposeful and indicates that they have been thinking about the ideas presented to them in the previous lesson. It also implies that the main idea or content on the Cuisenaire rod was not well understood; thus, putting forward a question for clarification was a
step towards filling their knowledge gap for future learning.
Data generated from teacher educators' questions inform the direction of the ongoing learning process, whiles questions raised by students activated their prior knowledge and helped them to elaborate on their learning. It can therefore be concluded that some teacher educators' questions influence students' participation and help the students to explore the topic, and motivated them to think aloud. Students learn differently; therefore, it is necessary and important that teacher educators know the kind of knowledge students bring to class prior to instruction, in order to prepare a lesson and assessment that meets the learning needs of the students. Classroom observations showed that the majority of teacher educators tried to elicit information about students’ knowledge on yet to be tackled subject matter (topics) through questions and answers.