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  • Writer's pictureKatie Lane-Karnas

Learning Sample: Math

Our state requires submitting examples of home study work that demonstrate learning. One of my favorite parts of working with families on this paperwork is getting creative about how to get these samples for kids who break our expectation of what learning "should" look like.

The easiest path is probably to print worksheets and have the child fill them out, maintaining a family's privacy and doing as little work as possible to fulfill the family obligation to report on homeschooling. But families have multiple reasons why this is a nightmare or impossible. A child who is resistant to simply filling out a stack of worksheets is exercising their intact self-worth and communicating a "no" in the face of a task that is somehow inaccessible to them. The family is watching a child's strengths and challenges over time, and in contrast to school, will not need the child to hit a brick wall in order to make daily tweaks and modifications so their child can learn and develop. Here's one example of how a learning sample for math can be generated, an idea that may spark ideas for families who need to get creative about having documentation of homeschool work.

Colorful Wikki Stix and unit blocks set up on a table to show a "greater than" problem.

Wikki Stix are colorful lengths of waxed yarn. They stick with gently finger pressing, and can be peeled up and repositioned over and over. We folded one in half and looked at the shape it made, flipped it around, etc. The kids compared quantities and positioned the greater than/less than symbol to show which amount is larger.

One child had a difficult time understanding how to memorize which way is greater than, and understood when shown that just like with words, we read math sentences from left to right, and she added a Wikki Stix arrow to remind herself. This setup is tactile, which makes it accessible for kids with visual impairment and kids who need time and help to develop an internal, visualized number sense.

Clipboard with paper and Wikki Stix greater than sentence stuck on.

The same style equation can be played with on a clipboard with paper. This is getting ready to remove the block manipulatives (or LEGOs, candies, beans, etc.) and replace them with a written numeral. Grab a photo of the child's work putting different amounts on either side of the equation, and adjusting the greater than/less than sign.

A paper on a clipboard has colorful Wikki Stix saying 10 is greater than 5.

For a child who can write numerals, the learning sample can show that. This can be done hand-over-hand, dictated, with fridge magnet numbers, with stamps, formed with Wikki Stix, with number stickers, or cut and pasted in place.

Handwritten math quantities are written by a parent and a child has made greater than/less than symbols.

Everyone can play with Wikki Stix and opportunities to consider application of greater and less than symbols can be adjusted for age and ability. When including a photo of nonconventional schoolwork, include a description of what the child was learning. (If I'm not sure, I google it.) For example:

Jenny learned to use signs of comparison with:

  • Place value into the ten thousands;

  • Multiplication and division expressions;

  • Addition and subtraction expressions;

  • Fractions with unlike denominators;

  • Solving for a variable;

  • Decimal place value;

  • Currency;

  • Weight on a kitchen scale;

  • Weight conversions;

  • Miles and kilometers;

  • Length of different stuffies/shoes/etc.

A ladybug stamp is shown to equal 2 on a paper. Math expressions using the ladybug as a variable are compared.

A child who loves to crack codes but is challenges with fine motor, writing, or becoming overwhelmed can work with higher level math (comparing expressions using variables) and focus on the solving without having their work break down completely because it is handwriting-heavy. Here the child can use their Wikki Stix greater than/less than symbol to stick in place on the paper to demonstrate understanding. If appropriate, the child can use a marker to trace right around the Wikki Stix symbol (it looks really colorful and cool) and peel it off to have written the symbol themself. For the learning sample, include in the description, "Jeremy showed which was greater, and read the math sentences accurately." If the child wants to create their own for you to try, get a photo of the problem they created for you and indicate "Jeremy learned to write math problems with expressions and signs of comparison."

Colorful Wikki Stix have been sculpted into flower and abstract 3D designs.

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