Walk into an early elementary school classroom and you are likely to see lots of manipulatives. From Popsicle sticks to Cuisenaire rods we have a strong intuitive sense that these objects should help children learn mathematics.

Although manipulatives can increase students’ attention, this attention may not benefit their learning. In fact, the very aspect of manipulatives that capture students’ attention—bright colors, visual appeal, realistic features—may be their downfall. Manipulatives that are more visually interesting or realistic can increase off-task behavior, such as building or sorting (1). This is especially true if students interact with that object in other contexts, such as during play time or outside of the classroom.

Students who learn with manipulatives can become too reliant on the object and context, and as a result, have difficulty transferring their knowledge to new contexts, different testing formats, or to abstract representations (e.g., algebraic expressions) of the problem

Getting children to apply what they learn in one class to another is a difficult task. The teachers I worked with called this “Johnny in a box”. So often what they “learned” in one class they were unable to apply in another. I tried a practical approach to teaching Excel to a class of eighth grade students by applying Excel to problems in their math book. I found I had to reteach math concepts that their math teacher claimed they already knew.

The technical name for this is transfer, there is a good Wikipedia article on the topic https://en.wikipedia.org/wiki/Transfer_of_learning
It remains a very controversial topic in educational psychology

I think transfer is essential to developing critical thinkers. That is why I loved teaching computer. Many projects centered around students using technology to solve real world problems or projects that extended what they were learning in other classes.

Getting children to apply what they learn in one class to another is a difficult task. The teachers I worked with called this “Johnny in a box”. So often what they “learned” in one class they were unable to apply in another. I tried a practical approach to teaching Excel to a class of eighth grade students by applying Excel to problems in their math book. I found I had to reteach math concepts that their math teacher claimed they already knew.

The technical name for this is transfer, there is a good Wikipedia article on the topic

https://en.wikipedia.org/wiki/Transfer_of_learning

It remains a very controversial topic in educational psychology

I think transfer is essential to developing critical thinkers. That is why I loved teaching computer. Many projects centered around students using technology to solve real world problems or projects that extended what they were learning in other classes.