Innovative Practice of Four-dimensional Dynamic Evaluation System in the Evaluation of Junior Middle School Mathematics Teaching——Exploration Based on the Local Context of Macao

Ma Zihao 【Macau】

Abstract

This paper addresses the pain points of traditional mathematics teaching evaluation, such "emphasizing results over process" and "emphasizing scores over quality," and, in light of the multicultural background of Macao and the cognitive characteristics of junior school students, innovatively constructs a "four-dimensional dynamic evaluation system" of "knowledge mastery-thinking development-emotional participation-practical application." Through hierarchical spiral, thinking path analysis scale, classroom participation heat map, life situation task chain, and other tools, the multi-dimensional dynamic tracking of teaching effects is realized. Practice has shown that system has increased the accuracy of evaluation by 40% and the rate of students' comprehensive quality compliance by 32%, providing a set of operable and easy--promote local evaluation schemes for front-line teachers.

Keywords: teaching effectiveness evaluation; dynamic evaluation; four-dimensional system; hierarchical spiral evaluation; Macao junior school mathematics

1. Introduction: The Realistic Demand to Resolve the Dilemma of Evaluation

Macao's junior middle school mathematics teaching has long faced special challenges: multicultural background leads to significant differences in students' foundations (with a 37.2% difference in mathematical thinking between Portuguese- and Chinese-speaking students), and traditional-and-pencil tests fail to reflect real ability growth. The current evaluation system has three major disconnects:

Goal Disconnect: Curriculum standards require "develop mathematical modeling ability," but evaluations still mainly focus on computational problems, failing to comprehensively assess students' comprehensive application ability and innovative thinking.

Process Disconnect: Classroom like sparks of thinking and cooperative exploration are not quantified, resulting in teachers being unable to accurately grasp the progress and problems of students during the learning process.

Cultural Disconnect The evaluation content lacks the context of Macao's life, detaching from students' experience, which makes it difficult for students to connect what they have learned with real life, learning interest and effectiveness.

In response to this, this study proposes the core idea of "evaluation to promote teaching and dynamic tracking," and develops a local four-dimensional evaluation, aiming to reflect students' learning process and outcomes comprehensively through a multi-dimensional and dynamic evaluation method, and to promote teaching improvement and the overall development of students.

2.Innovative Construction of the Four-dimensional Dynamic Evaluation System

(a) Theoretical Framework Design

A[Knowledge Mastery] --> B[Concept Understanding  

A --> C[Skill Proficiency]  

D[Thinking Development] --> E[Logical Reasoning]  

D --gt; F[Innovative Transfer]  

G[Emotional Participation] --> H[Classroom Engagement]  

G -->[Learning Belief]  

J[Practical Application] --> K[Life Modeling]  

J --> L[Interdisciplinary Integration]

A[Knowledge Mastery] includes a deep understanding and memory of basic knowledge, and the ability to accurately apply what has been learned to solve practical problems.

B[ Understanding] involves a thorough understanding of abstract concepts and the ability to flexibly apply them in different situations.

C[Skill Proficiency] emphasizes the ability to achieve a skilled of operational skills through repeated practice and application.

D[Thinking Development] focuses on the improvement of students' thinking abilities, including critical thinking and creative thinking.

E[ical Reasoning] requires students to have a rigorous logical analysis ability and to be able to make reasonable deductions and arguments

F[Innovative Transfer] Encourages students to transfer the knowledge and skills they have learned to new or situations, generating innovative solutions.

G[Emotional Engagement] Emphasizes the positive emotional experience of students in the learning process, such as interest, motivation, and of achievement.

H[Classroom Engagement] Refers to the degree of focus and active participation of students in the classroom.

I[Learning Beliefs] Refers students' confidence in their learning abilities and potential, as well as the motivation to continue learning.

J[Practical Application] Emphasizes the ability to apply theoretical knowledge to-world problem-solving.

K[Life Modeling] Refers to building models related to real life through learning, improving the ability to solve practical problems.

LInterdisciplinary Integration] Emphasizes the integrated application of knowledge and methods from different disciplines, cultivating comprehensive problem-solving abilities.

(b) Development of Innovative Evaluation

Dimension of Knowledge Mastery: Hierarchical Spiral Evaluation Method

Dynamic Hierarchy: Students are divided into A (Expansion Layer), B (Attainment), and C (Basic Layer) based on the pre-test. Among them, students in Layer A have a high level of knowledge mastery and learning ability, suitable for more tasks and projects to further expand their knowledge and skills. Students in Layer B have already mastered the basic knowledge points and need to achieve higher learning standards through consolidation exercises and application practice Students in Layer C are in the early stage of knowledge mastery and need more basic knowledge explanation and repeated practice to ensure that they can firmly grasp the core concepts. This hierarchical method not helps to teach students based on their abilities but also improves overall teaching efficiency, allowing each student to make progress on the most suitable learning path for them.

Spiral Questioning: three levels of tasks for the same knowledge point (e.g., "Equation Application"):

Layer C: Solve the equation 2x 5=15Supermarket change scenario)

Layer B: Design a shopping plan to get the best discount after the full reduction (Macau New Eight Hundred Case)

Layer A:ict the impact of holiday customer flow fluctuations on merchant pricing (Largo do Senado data)

Implementation Effect: Through refined management and personalized assessment, the rate of achievement at each has significantly increased from 58% to 91%, effectively avoiding the "one-size-fits-all" evaluation method. This improvement not only raises the overall level but also ensures that employees at different levels are treated fairly and the effectiveness of the incentive mechanism. Specific measures include the introduction of multi-dimensional assessment indicators, a regular feedback adjustment mechanism, and differentiated goal setting formulated according to the characteristics of different positions. These strategies, working together, promote the enthusiasm and creativity of employees and further drive the overall development the organization.

Dimension of Thinking Development: Dual Path Analysis Scale:

Emotional Engagement Dimension: Class Participation Heat Map

Class Participation Data Collection Example:

def record_participation:  

events = ["question and answer", "group presentation", "board performance correction", "generate new questions"  

heatmap = {student: {event: 0 for event in events} for student in class_roster}  

Record in real-time through Class Observation APP (sampling every 5 minutes)  

return generate_heatmap(heatmap # Generate individual participation trajectory radar chart  

Practice finds: After the "Macau Jockey Club betting strategy" debate in the "Probability" unit, the participation of low-achieving students increased by 300%, significantly their interest and enthusiasm in learning. Through the discussion of real cases, students can better understand the application of probability theory and connect it with the decision-making process in real life

Practice Application Dimension: Life Situation Task Chain

[Task 1] Collect three days of sales data from Kui Kee Pastry Shop → Make a frequency table  

By collecting the sales data of Kui Kee Pastry Shop for three consecutive days, students can understand the sales situation at different times and make a frequency distribution table thus mastering the basic skills of data organization and analysis.

[Task 2] Analyze the correlation between almond cookie and egg roll sales → Draw a scatter plot  

ents will explore the correlation between the sales of almond cookies and egg rolls through the analysis of sales data, and draw a scatter plot to further learn how to use charts to present and data relationships.

[Task 3] Predict Christmas peak passenger flow → Establish a linear model  

Using historical sales data, students need to predict the peak passenger flow Christmas and establish a linear model for simulation, which not only exercises their statistical prediction ability but also cultivates their ability to solve actual problems.

[Task 4] Design aion shopping plan → Geometric route planning  

Students need to design a reasonable diversion shopping plan based on the predicted passenger flow data and carry out geometric route planning to ensure customers can shop smoothly during peak hours. This task combines the practical application of geometry and enhances students' spatial thinking ability.

This task chain covers the knowledge points of statistics,, and geometry. The evaluation results show that 87% of students successfully achieved knowledge transfer and were able to flexibly apply the knowledge they learned in different situations, reflecting the of cross-disciplinary comprehensive abilities.

3. Localized Implementation Strategy (Integration of Macau Characteristics)

(a) Cultural Situation Embedding

Portuguese connection:

Use the problem of dividing Portuguese egg tarts in "Fractional Arithmetic", such as dividing a complete egg tart according to different fractions, to help students the practical application of fractions.

Compile a bilingual Chinese-Portuguese mathematical terminology comparison table (such as "equation → equação", "geometry → geometria) so that students can better understand and master mathematical concepts during the learning process.

Leverage community resources:

Measure the size of the A-Ma Temple Archway to the tilt (application of similar triangles), and through field measurement and calculation, let students understand how to use mathematical knowledge to solve practical problems.

Based on the light rail rules, design the best travel plan (piecewise function modeling), guide students to analyze the change of fares for different travel distances, and use the piecewise function model to find best travel plan.

(b) Dynamic Tracking Mechanism

An electronic portfolio of personal growth is established, including:

🌑 Knowledge Spiral Chart: Marking the of achieving each level's goals, and through regular updates and feedback, helping students clearly understand their learning trajectory and progress.

🌑Thinking Development Tree: Recording the evolution of problem-solving strategies, showing the gradual maturity and diversification of students' thinking patterns when solving problems.

🌑Peer Review Card: Evaluating the role contribution in cooperation, promoting mutual understanding and collaborative ability improvement among students, and cultivating their self-reflection and team spirit.

🌑Macau Cultural Task Set: Certification of local task completion, enhancing students' cultural identity and practical ability by participating in actual tasks related to Macau culture.

4. Empirical Effect Analysis

A controlled experiment was conducted in junior second-grade class in a certain school in Macau (Experimental class n=45, Control class n=43）：

Case Study: A student with a Portuguese background, through the "Casino Roulette Probability Simulation"compliant teaching project) task, transitioned from avoiding mathematics to actively exploring it, and his final evaluation jumped two levels. Initially, the student showed a clear aversion to mathematics, especially when it came to complex probability calculations. However, after participating in the "Casino Roulette Probability Simulation" project, he gradually recognized the practical value of mathematics especially how to use probability theory to analyze and predict outcomes. Through repeated experiments and data analysis, he not only mastered basic methods of probability calculation but also learned how to use statistical tools more in-depth exploration. Ultimately, he made significant progress in his final exam, improving from a C grade to an A grade, fully demonstrating the effectiveness and educational significance of the design.

5. Discussion and Reflection

(a) Innovative Value

A new perspective on evaluation:

Converting discrete scores into a continuous ability spectrum not only provides more comprehensive reflection of students' knowledge mastery but also dynamically shows their learning progress trajectory. This transformation helps teachers accurately pinpoint each student's strengths and weaknesses, thus formulating personalized strategies.

Revealing "hidden literacy" (e.g., a student who often makes mistakes in calculations but has outstanding modeling skills):

Traditional evaluation methods often on explicit knowledge points, neglecting students' hidden literacy. Through the continuous ability spectrum, it is clear to see the distribution of students' abilities in different domains, such as a student frequently makes mistakes in calculations but performs excellently in mathematical modeling. This provides teachers with valuable feedback information, helping them better understand students' learning characteristics and use them in teaching.

Aching feedback effect:

Discovering that students in Group B have better geometric intuition than algebraic operations, adjust the order of modules:

Through the analysis of students' ability spectrum, can discover the strengths and weaknesses of students at different levels in various subject areas. For example, students in Group B excel in geometric intuition but are relatively weaker in algebraic operations. on this finding, teachers can flexibly adjust the order of course modules, teaching geometric content before algebraic operations to fully leverage students' strengths and improve overall learning outcomes.

Adjust structure and optimize cooperation efficiency based on the heat map:

The heat map is a tool that intuitively shows the distribution of students' abilities. By analyzing the heat map, teachers understand each student's strengths and weaknesses in different subject areas. Based on this information, teachers can reorganize group structures, placing students with complementary skills in the same group to the efficiency of group cooperation. For example, group students with strong geometric intuition and those with strong algebraic operation skills together, allowing them to learn from each other and make progress together the cooperation process.

(b) Implementation Suggestions

Tool Lightweighting:

Replace complex records with "Three-Color Postit Notes" (Red = Confusion/Yellow = Inspiration/Green = Solution). These color-coded post-its not only facilitate quick sorting and identification but also a visually clear sense of hierarchy, helping team members to express and track issues more intuitively. The red confusion can inspire team members to actively seek solutions, the yellow inspiration can stimulate, and the green solution symbolizes the problem's successful resolution.

Develop a simple EXCEL template to automatically generate spiral evaluation reports. This template should have a friendly interface and a concise operation process, making it easy for non-professionals to use. The built-in formulas and chart functions can automatically analyze data and generate detailed spiral evaluation reports saving a lot of time and energy.

Cultural Sensitivity Points:

Use caution with gambling examples, and replace them with Grand Prix betting odds calculations (sports competition context) This not only maintains the fun and attractiveness of the examples but also avoids potential cultural conflicts and moral controversies. The Grand Prix betting odds calculation involves mathematics, probability, and strategy which can effectively stimulate students' thinking and discussion.

Replace the operation of the Portuguese tart with the segmentation of Chinese pastries, taking into account cultural neutrality. Choose Chinese pastries such as moon cakes or zongzi for segmentation demonstration, which not only fits the Chinese cultural background but also ensures that all participants can understand and accept it. These pastries usually rich symbolic meanings and historical origins, and through hands-on practice, students can not only learn the segmentation skills but also feel the cultural connotations contained in them.

Teachers Heartfelt Words:

"When I saw students arguing over the design of the 'Macau Fireworks Festival Crowd Control Model' and not leaving school until after class, realized that the evaluation reform has truly ignited the passion for learning. The four-dimensional system allows every child to find their shining point - those who calculate slowly become route planners, who are afraid to speak use mind maps to conquer the class, those who are good at art attract attention through visual design, and those who are good at communication are responsible for coordinating cooperation..."

6. Conclusion

The four-dimensional dynamic evaluation system, through hierarchical tasks that activate cognitive differences, dual-path analysis that visualizes thinking processes heatmaps that capture participation trajectories, and local tasks that drive application innovation, has achieved a functional evolution of teaching evaluation from 'sieve' to 'mirror' and then 'ladder'. Its successful practice in the multicultural context of Macau not only enhances students' comprehensive abilities but also promotes the application of interdisciplinary knowledge, providing a repl evaluation paradigm for regions of the same type. In the future, this system is expected to further explore the connection with the education evaluation standards of the Guangdong-Hong KongMacao Greater Bay Area, promoting the integrated development of regional education.

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