# Developing Proficiency When written to the level of “profound learning,” high priority learning standards (HPLS) may serve as year-long goals for students.  Guided through goal tracking graphs, I can… statements, and regular reflection on progress, educators can support student ownership of those HPLS goals.

Such long-term goals are intimidating, though.  The aim to build understanding and skills over the course of an entire school year is a massive undertaking for children.  So, how do we measure each student’s progress toward proficiency of those standards, without dwelling on the shortcomings of such a daunting aim in the form of a year-long goal?  On the path to the high priority learning standards, let’s guide students to attain understanding and skills designated by specific, developmental learning targets.  These smaller-scale marks provide opportunities for feedback, mini-victories on the road to profound learning.

Learning should be specified to the “profound level,” that is, students are able to apply their learning to new situations, to synthesize, solve problems, create knowledge, and cultivate and utilize the full range of their capabilities.

A developmental series of learning targets, all aimed toward a certain HPLS goal can support a growth mindset – that progress is possible, measurable, and valued.  Examples of such learning targets for grade 3 math are below.

High Priority Learning Standard

3.3F Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number line.

Learning Targets

1. The student can represent equivalent fractions with denominators of 2, 4, and 8 using concrete models (fraction circles, pattern blocks, drawings, geoboards).
2. The student can represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects or pictorial models.
3. The student can represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines.

Notice the developmental progression of both the denominators and the models for fractions, beginning with an area model (fraction circles, pattern blocks, …) aiming toward the more challenging linear model (number lines).

High Priority Learning Standard

3.3G Number and operations. The student applies mathematical process standards to represent and explain fractional units. The student is expected to explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model.

Learning Targets

1. The student can use a concrete model to represent two fractions that are equivalent  (fraction circles, pattern blocks, drawings, geoboards).
2. The student can explain that two fractions are equivalent if and only if they are both represented by the same portion of the same size whole for an area model (fraction circles, pattern blocks, drawings, geoboards).
3. The student can explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model (fraction circles, pattern blocks, drawings, geoboards).

These learning targets on the path to high priority learning standards provide additional benefits for educators and parents, as well:

• Knowing the smaller steps toward the goal, educators may design learning experiences with intentional desired outcomes, measures of success, and opportunities for specific feedback.
• The targets are valuable communication pieces for parents.  Yes, the students will achieve this (HPLS) profound level of learning by the end of the school year, but in the mean time the students will be able to do this, this, and this (targets).