Towards a Comprehensive Meaning for Formative Assessment: The Case of Mathematics Athanasios Gagatsis, Theodora Christodoulou, Paraskevi Michael-Chrysanthou, Iliada Elia, Elena Kiliari UNICA, Rome, 15-16 December 2016

Adopted Meaning & Scope Formative Assessment Definition Formal & Informal Techniques Adopted Meaning & Scope

Assessment Formative Assessment NCTM (1995) “the process of gathering evidence about a student’s knowledge of, ability to use, and disposition towards mathematics and of making inferences from that evidence for a variety of purposes” Harlen (2000) “children have a role in assessment for this purpose since it is, after all, the children who do the learning” assessment must be formed “for” learning and not “of” learning the use of formative assessment (or assessment for learning) leads to higher quality learning (Wiliam, Lee, Harrison & Black, 2004)

Formative assessment including diagnostic testing is a range of formal and informal assessment procedures employed by teachers during the learning process in order to modify teaching and learning activities to improve student attainment. It typically involves qualitative feedback (rather than scores) for both student and teacher that focuses on the details of content and performance. It is commonly contrasted with summative assessment, which seeks to monitor educational outcomes, often for purposes of external accountability. http://en.wikipedia.org/wiki/Formative_assessment

Definitions Teacher – Student interaction Black & William (1998): Formative assessment is ‘‘the method that represents all classroom activities that are performed in classroom settings by either educators and/or their students and employ both of them in the process’’. Modifying learning Van De Walle, Karp & Bay-Williams (2013): Formative assessment is ‘‘an along the way evaluation that monitors who is learning and who is not and helps teachers to form the next lesson”. Wiliam (2007): ‘‘To be formative, assessment must include a recipe for future action’’.

Definitions Feedback Cauley & McMillan (2010): Formative assessment is defined as ‘‘a process through which assessment elicited evidence of student learning is gathered and instruction is modified in response to feedback’’. Sadler (1998): Formative assessment refers to ‘‘assessment that is specifically intended to provide feedback on performance for improving and accelerating learning’’. Hattie (2009): A powerful influence of formative assessment on achievement is the meaningful feedback from students as to what they know and where they make errors or have misconceptions.

Definitions “A process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes.” Popham (2008)  

Adopted Meaning & Scope Formative Assessment Definition Formal & Informal Techniques Adopted Meaning & Scope

Formal and Informal Formative Assessment provides evidence about students learning Formal Informal (Bell & Cowie, 2001; Duschl, 2003; Shavelson et al., 2003) students’ learning is evident during the course of a teacher’ s daily activities

Formal and Informal Formative Assessment information is obtained based on the whole class it usually begins with students carrying out an activity designed or selected by the teacher (information may be more precisely collected) practices take the form of curriculum embedded assessments can take the form of direct questioning, quizzes, brainstorming, generation of questions, and the like (Bell & Cowie, 2001) The implementation of this type of assessment is planned in advance by the teachers and it can be conducted at the beginning, during, or end of a unit.

Formal and Informal Formative Assessment can take place in any interaction between teacher and his/her students (anytime) can engage whole class, small group or individual interactions not to be planned in advance, because it can happen at any time there is no specific activity designed for students Teachers cannot predict exactly when they will be able to gather evidence about students understanding during the lesson of non-planned activities, but they can give students various opportunities for doing so (e.g., by creating more interactions in class, group discussions, or informal observations).

Formal and Informal Formative Assessment Both types of formative assessment (formal and informal) involve gathering, interpreting, and acting on information. The difference between formal and informal formative assessment lies in how much planning is done and the type of planning required.

Adopted Meaning & Scope Formative Assessment Definition Formal & Informal Techniques Adopted Meaning & Scope

Techniques Cauley & McMillan (2010) Informal observations Oral questions while content is taught Providing clear learning targets If the information from the observations and questions to students is accurate, the teacher identifies instructional adjustments that can help improve the students’ learning.

Techniques Teaching Quality Papers – General Teaching Council for England (2011) Questioning techniques Feedback strategies Sharing of learning goals to students Peer and self-assessment

Assessment process NCTM (1995) Common Core State Standards

Adopted Meaning & Scope Formative Assessment Definition Formal & Informal Techniques Adopted Meaning & Scope

Purpose Techniques Results Teachers Students assessment FOR teaching and learning regulates teaching-learning process establishes a dialogue between teacher and student teaching methodologies which can respond effectively to different learning times for each student their different learning styles their zones of proximal development formative feedback feed forward allows teachers to reflect on and modify their own practices designs educational interventions Involves the outputs of teacher’s choices (transposition of mathematical contents, interface between contents and methods) Students students to acquire the basic skills of a discipline identify the strengths and weaknesses of student’s learning gives information, feedback and feed forward – in and outside of the classroom – related to the development of mathematical life-skills promotes students’ ability for self-assessment and peer-assessment learning for all students through differentiated teaching (different rhythms and different teaching and learning strategies) students’ active participation in the teaching-learning process involves the student in the analysis of own errors/ weaknesses

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