This essay focuses on stages of development. Figure 5.7 Spatial Reasoning Learning Progressions Spatial Reasoning

stages of development

Assessing Spatial Reasoning You can assess students’ ongoing demonstration of spatial reasoning using the Talent Aptitude Learning Progressions. These stages of development provide a systematic way to describe and document evidence and provide feedback. Chapter 7 provides a detailed process for assessing talent aptitudes. Figure 5.7 Spatial Reasoning Learning Progressions Spatial Reasoning Emerging Progressing Advancing Teacher Rubric Recognizes and remembers simple images; visualizes three-dimensional objects and identifies relationships.

Recognizes and remembers complex images; visualizes and manipulates three-dimensional objects to solve problems. Mentally manipulates, constructs, and interprets relationships among three-dimensional objects to solve problems. Student Rubric I recognize and remember images and threedimensional objects. I visualize, remember, and understand relationships among three-dimensional objects. I understand the relationships among three-dimensional objects and mentally manipulate them to solve problems.

5. Mathematical Reasoning

When people react negatively to the subject of mathematics, the reason is usually based on the way that it was taught: We learned the rules without the reasoning.22 Mathematical reasoning is sensemaking—the critical thinking that enables us to recognize patterns; develop arguments; explore, explain, and evaluate mathematical arguments; and communicate insights.23 While procedural understanding is important, we must link it to conceptual understanding in order to solve problems.

Advanced mathematical reasoning is a key aptitude of STEM innovators, but it is not the only factor. Research shows that young people with high mathematical aptitude who also had engaged in rich and varied STEM experiences were more likely to achieve at high levels in STEM careers.24 All learners can develop their mathematical reasoning, beginning with the process of engaging their preconceptions about learning mathematics.

Details;

Firstly, be sober

secondly, be integrity

Thirdly, stem

further, be creative

Further, be sober