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THE ANIE
Assessment of Numeracy in
Education.
Shelley Wojcik
March 31, 2015
For one of my school projects in Education 300, I needed to observe a teacher in their own
classroom. The first lesson was grade four math. The teacher gave each student a single
worksheet, and on it was one math problem. Each student got out their pencil crayons and
felts, started cutting and folding the worksheet, and remained fully engaged while working for
fifteen minutes on one question. I noticed the teacher taught this math problem in a series of
steps and after each step the teacher reminded the students of the rubric for this activity and
made sure they knew what was expected of them in order to achieve success. The second step
was solving the question. What could possibly be next after giving the correct answer? As it
turns out, solving the question was just the beginning. The real solution is understanding the
problem. This backwards way of approaching math is called the ANIE.
ANIE is an acronym for Assessment of Numeracy in Education and was created in 2005 by Kevin
Bird and Kirk Savage, two school administrators from British Columbia. It was their goal for all
students to be taught math learning outcomes from grade 1-12 with real world applications,
and to help teachers to achieve this goal. Bird and Savage have followed the latest brain-based
learning research and BC Performance Standards to design this effective, simple, and relevant
tool for teachers and students. Since the ANIE material has been available on line in 2006, it
has found homes in classrooms in Canada, the United States, China, South Korea, Israel, and
India. Throughout the years it has been revised, and changes and additions were made with
the help of pilot groups’ feedback. A primary specific ANIE junior was created and is used
extensively and effectively for students with special learning needs. (Sibbald, 2014)
Traditionally, math word problems start with a real-life situation. Some students lack reading,
vocabulary and comprehension skills of word problems so this added complexity prevents them
from being able to focus on the math. The ANIE turns this traditional model upside down by
starting with a math question rather than a word problem. Eliminating language barriers allows
students a greater understanding of the math itself by enabling them to use their own words to
explain their thinking. Students develop their own real life word problems which promotes a
deeper level of cognition, engagement and a long term understanding of the material. (Bird
and Savage, 2014) The relationship model below, shows the link between literacy and
numeracy and can help in understanding how applying language arts to math can strengthen
comprehension.
The ANIE template includes estimation, calculation, representation, explanation, application to
real life, and reflection. It is an assessment for, of, and as learning that allows teachers to
effectively plan instruction, to assess student comprehension, and to encourage student
reflection, respectively. The step by step strategy and the incorporation of various learning
tools in the ANIE, is a unique scaffolding approach to math comprehension and problem
solving, and allows students to be actively engaged and make connections to their own lives in
order to facilitate learning. (Bird and Savage, 2014) The value of the ANIE is not only in its
assessment properties, but as a teaching tool to increase comprehension in all learners.
The ANIE is broken down into several steps, assessing a students’ level of understanding with
one single math question.
1.
The student is asked to estimate the question of the day. For an example, (321 x 4). This helps
student’s work on mental math, as the goal is to have the estimated answer within 10 seconds.
2. Students then explain the process of how they estimated with a partner. When required to
explain their thinking, students increase their comprehension and retention of the
material. A/B partner talk also allows students to become self-aware, develop paraphrasing
and listening skills, and become metacognitive learners. (Bird and Savage, 2014)
3. The student solves the algorithm of the question, practising math fluency.
4. Students then draw a picture to represent the question. A clear picture that evidently
demonstrates the question, with captions, numbers, or explanations to clarify.
5. Students then explain their picture to an AB partner.
6. Next, they write out a real-life example for the math question. This is a time for students to be
creative and original with their comprehension.
7. Then then share their real-life example with an AB partner.
8. Students take the time to discuss and reflect in their learning what was easy or hard, and make
goals for next time.
As developing educators, we are taught that learning is multidimensional and set within a social
context. The ANIE is a practical application that incorporates these cognitive learning theories
and many more. It encourages creative thinking and writing, social skills, connecting to real-life,
sharing ideas with others, active thinking and reflection. Each time a student completes an
ANIE, they strengthen their neural connections between brain cells, and consistency allows
these pathways to be more efficient in transmitting messages within the nervous system.
(Auger and Rich, 2007) Not only is the ANIE relevant to learning, it is also an effective
assessment tool which helps teachers identify their students’ math comprehension while
supporting gaps in their learning. It provides an opportunity for teachers to reflect on their
teaching to ensure no students fall behind and to identify problems quickly for
intervention. The ANIE also helps identify students that can go deeper in understanding a
concept and move beyond expectations in math. Gaps in learning are not always apparent
from testing correct answers. Many students get the correct answer without an understanding
of concept or procedure. The ANIE helps students to represent answers in different ways and
to identify multiple solutions and approaches which develops comprehension. (Bird and Savage,
2014)
It is common for developing educators to feel reluctant about teaching math. Many teachers
are intimidated by the subject, sometimes because of past experiences in school or possibly
because of a general insecurity with the material. Many teachers who have mathematics
anxiety inadvertently pass it on to their students and this lack of passion and self-confidence for
math can negatively influence their students’ mathematics achievements. (Johnson and
vanderSandt, 2011) The ANIE can change the way teachers think about math, the way they
teach math and in turn how students learn math.
Paul Wojcik, a grade 4 teacher at Vedder Elementary, passionate about mathematics, tried the
ANIE in conjunction with the math pilot group within the district, connecting the effectiveness
of the ANIE program while also teaching the JUMP math program. After the first year, Wojcik
noticed a confidence boost in all learners when it came to the applicability of the math they
were learning in examples of real-world situations. In his previous four years of administering
the Foundation Skills Assessment (FSA), testing showed that on average, ~10% of his class was
not yet meeting expectations, ~80% of his class was meeting expectations, and ~10% of his
class was exceeding expectations. Since using the ANIE, Wojcik’s last two years of FSA testing
have seen no students’ not yet meeting expectations, and approximately 68% exceeding
expectations.
Looking at these results, it’s evident that students have vastly improved in their comprehension
of the applicability of math into real life situations. They are exposed to them daily, are looking
for ways to describe math in real life ways, and feel far more confident when introduced to
challenging math situations. Wojcik states, “When speaking with the teachers that have my
students from the previous year, they’ve noted that for the first time in years, students that are
in grade five are ‘totally getting math’. Combined with JUMP math for its fluency, I feel that
ANIE should now be considered ‘Best Practice’ for increasing math comprehension at the
elementary level.”
It seems like most teachers at the elementary level who are teaching students math skills, focus
primarily on fluency. They practice addition, subtraction, multiplication and division religiously,
try to have them work on their math facts each night, and usually by the end of the year they
hope the fluency is built in so they can recall it quickly for next year. This is similar to spelling
lists that you learn on Monday morning, practice spelling them all week, and master them for
the Friday assessment. Quite often students do very well on the spelling test on Friday, but
often the comprehension and usage of the words is ignored. Next year, will they be able to
spell it? Will they know what the word means, or how it’s used? It’s the same with working
purely on fluency as a math practice. You definitely need fluency, but is best served when
bridged effectively with comprehension. (Wojcik, 2015)
Wojcik focuses on the numeracy portion of his curriculum with the ANIE. He states, “I’ve found
some ways to effectively use the ANIE for other curricular areas (graphing, patterning, algebra,
etc.), but I find that it can sometimes confuse nine year olds even more when trying to create
estimates for patterns, or real life questions for algebra at this age. Not that it doesn’t have its
place in those areas of the curriculum, but I feel that my time is best served working on the
core skills that I want kids to carry with them as they move on. A strong foundation in
numeracy will serve them better when they are tasked with higher thinking challenges later on
in their middle school years and beyond.”
For Wojcik, it takes about two months to teach the steps required to fully work through an ANIE
question. After that, through the gradual release of responsibility, students can work through
an ANIE question in about 15 minutes each morning, which keeps the skills sharp, and the
comprehension high. Wojcik builds in lots of silly, fun real life questions, celebrates unique
ideas, and has even helped create thematic ANIE worksheet pages for his own class. Wojcik
states exuberantly, “Nothing like having fun while learning math!”
Bird and Savage have created a revolutionary and exciting new approach to teaching and
learning math. The ANIE helps students and teachers bring back a passion for learning math
that has unfortunately been lacking for years. It shows how a simple change of instruction and
some daily time devoted to the process, can bring about a shift in students and teachers
outlook on math. Building confidence in teaching and learning any subject can bring about
change and positively effect results. It is important for educators to understand the significance
of such professional development and forward thinking in our community.
References
Auger, Wendy Frood and Rich, Sharon J. Curriculum Theory and Methods. John Wiley & Sons,
Canada, Ltd. 2007.
Bird, K., and Savage, K. BCPVPA Admininfo. “The Big Idea.” BC Principals and Vice Principals
Association. Vol 21, No 2. Dec 2008.
Bird, K., and Savage, K. The ANIE: A math assessment tool that reveals learning and
informs teaching. Markham, ON: Pembroke Publishers. 2014
Johnson, Beth and vanderSandt Suriza. IUMPST: The Journal. Vol 5 (Teacher Attributes), “Math
makes me sweat” The Impact of Pre-Service Courses on Mathematics Anxiety.
December 2011
Savagebird Assessments, ANIE-Assessment of Numeracy in Education. WEB. 24 March, 2015
Sibbald, Tim. Ontario Mathematics Gazette. “Turning Problem solving Upside Down”-Book
Review of: The ANIE. Vol 53. No 1. 28, Sept. 2014
Wojcik, Paul. Personal Interview. 24 March. 2015.