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

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

3. 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)

4. 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.

5. 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’’.

6. 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.

7. 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)

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

9. 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

10. 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.

11. 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).

12. 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.

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

14. 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.

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

16. Assessment process
NCTM (1995)
Common Core State Standards

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

18. 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

19. Thank you for your attention!
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