It’s always fascinating to observe the variety of strategies students develop and employ when tackling mathematical tasks. Ordering and comparing decimals is a prime example. Despite engaging in the same shading activities and interactive comparing games, the application of these experiences to individual student thinking reveals a wonderfully diverse range of approaches within the classroom. In our recent assessment focused on Comparing And Ordering Decimals, the spectrum of student thinking was truly remarkable and insightful.
One of the most prevalent strategies observed in student work involved focusing on the tenths place value. Students initially considered the number of tenths present in each decimal. This approach aligns directly with our shading activities, where we emphasized representing whole tenths, partial columns for hundredths, and further subdivisions for thousandths. Therefore, it’s logical that many students would naturally start by comparing the tenths digit as their initial step in ordering decimals.
Another interesting strategy that emerged was converting decimals to fractions, specifically with a denominator of thousandths. One student, in particular, demonstrated a clear comfort level with fractions, opting to convert each decimal into its fractional equivalent with thousandths as the common denominator. It’s noteworthy that this student preferred to work with fractions, even though converting to decimals with thousandths would have been equally straightforward. This highlights how students leverage their individual strengths and preferences when problem-solving, even in comparing and ordering decimals.
One student effectively utilized the hundredths grid concept verbally to explain their decimal comparison process. Their explanation included descriptive terms like “blocks” and “1/2 blocks,” referencing the visual representation of decimals on a hundredths grid. This approach is valuable as it connects the abstract concept of decimals to a concrete visual model. A follow-up with this student to explore if they connect the “1/2 block” to the value of five thousandths would be a beneficial step in solidifying their understanding of decimal place value when comparing and ordering decimals.
The strategy, “I thought about it like whole numbers,” initially raised a slight concern. If a student were to misinterpret this and order decimals based solely on the digits as whole numbers (e.g., incorrectly ordering .6, 0.8, .55, .125, .875), it would indicate a fundamental misunderstanding of decimal value. However, further examination revealed that this student was actually multiplying each decimal by 1000, effectively converting them to whole numbers for comparison, and then implicitly ordering the original decimals based on this whole number comparison. This sophisticated approach, while initially appearing simplistic, demonstrates a deeper understanding of decimal place value and magnitude. Revisiting this strategy with the student to explicitly discuss the multiplication by 1000 and its effect on place value would be a valuable teaching moment for comparing and ordering decimals.
Finally, a number of students employed percentages as a comparison tool. This demonstrates a strong connection to our earlier work on fractions and percentages using the hundredths grid. Converting decimals to percentages provides another accessible way for students to conceptualize and compare decimal values, linking back to previously learned concepts and reinforcing the interconnectedness of mathematical ideas when comparing and ordering decimals.
This exploration of student strategies for comparing and ordering decimals provided a refreshing and insightful way to resume learning after a break. Witnessing the diverse approaches students take to solve problems underscores the importance of varied teaching methods and the power of understanding individual student thinking in mathematics education.
