In creating the Number Agility assessment, the goal was to create as fair of an assessment as possible for student and to follow the guidelines laid out in Classroom Assessment Standards for PreK – 12 Teachers (Klinger, et al., 2015). Numerous other sources were consulted while creating the assessment to ensure that the assessment is fair for all students and the questions were structured in such a way that all students could access them. The TIMSS guidelines provided valuable steps for creating questions and ensuring that steps were taken towards validity.
Choice of Content
The content of this assessment has been selected based on multiple sources including Clement and Samara’s Learning Trajectories, Western Australia’s First Steps in Mathematics, the British Columbia mathematics curriculum and the SD #35 Prioritized Essential Standards in Mathematics Learning document. By comparing these sources, it was possible to determine which skills belonged not only at each grade level but also the sequence in which they develop. There are slight variations in the skills between the academic articles and the BC curriculum when it comes to place value understanding, in this assessment place value understanding has been correlated to the research rather than the BC curriculum. This decision was made due to the ambiguous wording of the BC curriculum when it comes to determining place value understanding and the largest number student should be working with, for the purpose of this assessment it has been decided to name the place in which students are working i.e. Ten thousand or millions rather than the maximum for clarity. The content chosen for this assessment has been aligned with the BC curriculum and is sequential with the skills in each level and assessment building on the one before.
Assessment Format
This assessment has been formatted to allow students the opportunity to represent their learning in multiple ways and to give students the opportunity to demonstrate their skills multiple times. It was also a conscious decision not to use a digital format for the assessment. The choice not to use digital forms was made to ensure equity between students and different classes or schools implementing the assessment, students have varied levels of familiarity with devices, the internet is frequently unreliable in schools and choosing a digital assessment requires that teachers have the technical proficiency to trouble shoot the technology and support student use. There is also the issues of access to devices in schools and simply having enough devices for each student to have their own. The assessment has been formatted to incorporate elements that are familiar to both teachers and students, by using familiar formats in a written component and interview teachers and students are able to focus on the work instead of the format. An additional reason for the choice of using a combined written and oral format is that students may represent their learning better in one form or the other and may also experience test anxiety or math anxiety when completing portions of the assessment. Through out the assessment care has been taken to remove bias where possible and create something that is fair for all learners. There is an absence of “word problems” in this assessment as those have the highest possibility of including bias on the assessment due to them requiring students to have specific background knowledge to interpret the question and there for become reading comprehension tasks rather than math tasks.
Student Booklets
The booklets have large white spaces allowing students to have space to show their thinking without feeling cramped. Visuals on the pages have also been kept to a minimum and are only used when they communicate information needed to solve the problem. Reducing visual clutter allows the student to focus on the task being assessed.
Interview
The interview was again created with minimizing the amount of academic language in mind. With the exception of some new ELL students, it can be assumed that students from very young ages understand being asked to count, or the question of how many dots do you see? The interview was created to be conducted one on one with the student. This individualized format allows the student to show what they know without the distraction of peers or feeling the need to compete with classmates. An individual interview also allows the student to answer based on their own thinking and ideas without being influenced by classmates or feeling the need to change their answer to match that of their peers.
Question Construction
Great care has been taken to ensure that the questions and performance tasks in this assessment utilize the simplest language possible to ensure that the assessment retains content validity by only assessing the number sense concepts. The use of simple language supports many students’ learning needs and fosters a Universal Design for Learning approach to curriculum and assessment. To ensure construct validity there are multiple opportunities to demonstrate each skill, with the exception of subitizing students will demonstrate their understanding across all five strands in both the written and oral assessments. While many authors argue that reading skills are irrelevant to the constructs being assessed on a math assessment (Reardon, Kalogrides, Fahle, Podolsky, & Zarte, 2018) care has been taken to reduce the need for reading comprehension skills to support the learning needs of all learners.
Universal Design for Learning and English Language Learner Considerations
“Scaffolding an exam does not reduce the academic standards. It simply makes the instructions more comprehensible and helps students produce more accurate responses. “ (Huynh, 2023) When constructing the assessment, it was necessary to ensure that the assessment would be not only accurate for all students but accessible. Some of the features for keeping the assessment accessible to all include keeping the amount of text on the page to a minimum and using the simplest vocabulary possible to accurately give directions. Many questions have a large amount of workspace for students to show their work as well as there being significant amounts of white space on the assessment pages. Fonts have been kept simple and clip art has only been used where necessary to convey information or as part of a question. There is no extraneous decoration on the assessment pages to allow for white space to reduce the amount of visual information students are processing.
“Universally employable diagnostic tools are yet lacking, as current test batteries for basic mathematics assessment are based on verbal instructions. However, prior research has shown that performance in mathematics assessment is often dependent on the testee’s proficiency in the language of instruction which might lead to unfair bias in test scores,” (Greisen, et al., 2018) constructing the assessment to consider the need for reduced language requirements was key to allowing the assessment to be accessible for ELL students as well as for considering strategies to The absence of word problems also reduces the need for cultural references and knowledge. Choosing not to include word problems not only reduced the need for ELL students or new Canadians to understand Canadian culture but also serves to ensure the focus of the assessment is on number sense and not reading.
In some cases, using Google Translate or another spoken translator app may be needed to conduct the interview portion if a student is new to Canada (level 1 ELL student) and has limited English communication skills. Using a translator tool or inviting a translator to join you for the interview should be done with the support of the ELL or International Student team.