Tag: formative assessment

Posted in Assessment

Teach and assess for conceptual understanding

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To teach for conceptual understanding requires assessing for conceptual understanding. The principles that guide teaching for understanding must be the same principles that should guide assessment. What are some of these?

  • Open-ended, problem solving tasks
    To teach for conceptual understanding, it is not enough that students engage in problem solving task. The tasks should be (1) open-ended which means that it can be solved in many ways using a range of concepts; (2) accessible, that is , not too easy or too difficult but just beyond the students ability; (3) can be extended by changing conditions in the problem so that it can be used for building concepts and for making synthesis and generalization; and, (4) the task should encourage creativity in the problem solver. These, together with right amount of scaffolding from the teacher and assessment tasks possessing the same characteristics is a perfect recipe for understanding mathematics conceptually.
  • Activities that promote mathematical communication
    Mathematics is a language that enables us to communicate ideas with conciseness, clarity and precision both in oral or written form. Students learning experiences should always aim at developing this capacity. They should be given opportunities to talk about mathematics, to speak mathematics, and communicate mathematically through its written symbols.  These are possible with the right mix of collaborative and individual work. Click this link for sample. This also implies that assessment should focus not only on the knowledge the students are acquiring but also on their skill on communicating this knowledge.
  • Tasks that build on students’ previous knowledge
    Teaching should build on the knowledge that students already have. This does not mean simply putting something on top of what they know. Knowledge has to be connected with other knowledge from within and from without. The more connections there are, the more robust is the understanding. Conducting formative assessment can provide teacher with information on how to structure the lesson to help students make connections. Another strategy which I highly recommend is to teach via problem solving. Click here for sample lesson.
  • Discussions that respects reason
    Mathematics is a way of thinking logically and methodically. As such, classroom culture that respects reason must be created both in the teaching and in assessing. Group or whole class discussion and assessment rubrics should give appropriate feedback to the students as to the way they reason and build on each others reasoning or on each others opinion.
Posted in Assessment, Curriculum Reform, Mathematics education

Assessment for learning – its genealogy

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IN the beginning there was only diagnostic and summative assessment. Diagnostic assessment was supposed to share power with summative assessment in the classroom but never really attained equality with it not because teachers did not want to give diagnostic assessment but because stakeholders (parents and state) are more interested with statistics and well-defined label of students’ level of learning as measures of return of investments.

One glorious day, the education community had a dream. It dreamt that in the teaching and learning process, the students have much to contribute especially in the what and in the how they will learn! Thus formative assessment was conceived and born. Formative assessment shifted the focus of assessment from simply a process for collecting information about the learner to it being an integral part of the teaching- learning process. But the education community discovered a bug in the formative assessment.  At the end of the day, it couldn’t tell whether there was really learning that occurred or not because the teacher did not have the data of students’ initial understanding.  Actually they do only that the collection of the data is not “scientific” enough for educators. Thus, diagnostic assessment was resurrected and assessment for learning, was born.