Geometry is essential material to be learned in mathematics (NCTM, 2000; Abdullah & Zakaria, 2013) [
Some researchers (Clements & Batistta, 1992; May & Smith, 1998; Kondor, 2007; Bosnyak & Kondor, 2008; Sarama & Clements, 2009; van de Walle, Karp, & BayWilliams, 2010) [
Many researches (e.g., Unal, Jakubowski & Corey, 2009; Bruce & Hawes, 2014; Fajri, Johar, & Ikhsan, 2016) [
Prior researches (e.g., Erdogan & Durmus, 2009; Abdullah & Zakaria, 2013; Bansilal & Naidoo, 2012) [
However, there are still many teachers who rule out spatial reasoning, since they only assume that spatial reasoning does not significantly affect students’ score (Moss, Hawes, Naqvi, & Caswell, 2015 [
Referring to prior researches (e.g., Pruden, Levine, & Huttenlocher 2011; Yilmaz, 2009; Mulligan, 2015) [
Many researchers (e.g., Erdogan & Durmus, 2009; Abdullah & Zakaria, 2013; Astuti, 2015) [
The development procedure follows Analyzing, Designing, Developing, Implementing, and Evaluating stages (ADDIE; Branch, 2009) [
In the analysis stage, we collected information about the needs, the character of students and mathematics topics. They gave insights on the problem, i.e., the limited of mathematics resource in the vocational school to improve spatial reasoning, to be solved. The next stage is to design lesson plans and worksheets using van Hiele theory and oriented toward students' spatial reasoning.
The thinking levels of student was directed to geometric transformation, namely: 1) thinking level 0: students are able to understand the shape of geometric objects in the Cartesian plane; 2) the thinking level 1: students are able to identify the characteristics of geometric transformation and transformed geometry; 3) the thinking level 2: students are able to think about the types of transformations to geometry objects, as well as the relationships and differences between the transformations performed; 4) the thinking level 3; students are able to understand the concept presented through the examples until simple proof; 5) the thinking level 4: students are able to solve complex problems
Table 1. The indicators of spatial reasoning


Spatial orientation  Students are able to think and determine the shape of a plane 
Spatial visualization  Students are able to know transformation shape or position of an object 
Mental rotation  Students are able to know transformation of a plane and a solid based on its rotation direction 
Spatial relation  Students are able to know the spatial shape or relationship between parts of the plane 
Spatial perception  Students are able to know the parts of a plane or a solid in a vertical or horizontal position 
In the development stage, we started preparing lesson plans and worksheets followed by expert validation. Expert validation aimed to determine the feasibility and validity of the product development. We used



Spatial orientation 
Information, guided orientation, explication, integration Levels of thinking: 03 
Students are directed to think and determine the shape of the geometry object, its parts, and characteristics of geometric transformation 
Spatial visualization  
Spatial perception  
Spatial relation 
Free orientation, integration Level of thinking: 3 
Students are given questions, to improve their understanding of geometry object’s shapes after transformation 
Mental rotation 
Guided orientation, explication, integration Level of thinking: 4 
Students are directed to think and understand of rotation’s geometry object 
After the developed product was declared feasible, then lesson plans and worksheets could be implemented in the school. The last stage of product development is to evaluate the lesson plans and worksheets that have been tested to determine the practicality and effectiveness. If the product did not fulfill the criteria of practicality and effectiveness, then lesson plans and worksheets were revised and enhanced before using in the research. Nieveen (1999) [
The instruments in this research were validity instrument, practicality instrument, and spatial reasoning tests for effectiveness. The practicality of the instructional package was measured by three instruments: 1) practicality sheet by teacher, the questioner consisted of 23 items to examine the appropriateness of instructional package based on van Hiele’s phases to facilitate spatial reasoning and the ease of application in learning process; 2) student’s practicality sheet, the questioner consist of 16 items about benefits and the ease of student’s worksheet; 3) sheet of learning observation should be ≥89%
Five items of spatial reasoning test measure the effectivity aspect. These test items were based on the indicators of spatial reasoning. Question 1 was to examine students’ spatial orientation, so we can determine students’ reasoning capability to determine the shape of a plane. Question 2 was to determine students' spatial visualization which makes students able to know transformation shape or position of an object. Question 3 was about mental rotation to determine students' reasoning capability of transforming (change) a plane and a solid based on its rotation direction. Question 4 was for spatial relation, examining students reasoning for the spatial shape or relationship between parts of the shape. Question 5 for spatial perception, examining students' ability to identify the parts of a plane or a solid in a vertical or horizontal position.
This research collected both qualitative and quantitative data. The qualitative data was perceived from the result of validation sheet, the practicality assessment by teachers and students, and the learning activity sheet. It was then converted into quantitative data.


X is greater than x̅i+2sbi  Very good 
X is greater than x̅i+0,8sbi and less or equal to x̅i+2sbi  Good 
X is greater than x̅i+0,4sbi and less or equal to x̅i+0,8sbi  Fair 
X is greater than x̅i+0,8sbi and less or equal to x̅i+0,4sbi  Poor 
X is less or equal to x̅i0,8sbi  Very poor 
Notes:
X : empirical score
x̅i : ideal mean score = 1/2 (max score + min score
sbi : Standart deviation = 1/6 (max score  min score)
(Maximum ideal score = item x highest score )
(Minimum ideal score = item x lowest score)
This research aimed to develop an instructional package which comprises lesson plans and students’ worksheets based on van Hiele theory and oriented to spatial reasoning. The instructional package was developed to facilitate spatial orientation, spatial visualization, and spatial perception by providing an illustration or example of the application of transformation principle that occurs around students and on vocational materials. Then the spatial relation component can be facilitated through the provision of direct or written questions. Such activities can assist students in sharpening their thinking to know and determine the shape of the plane, its parts, and the transformation of a geometry plane.
The developed worksheets have general information and illustrations related to the topics with the aim of helping students to reason spatially. Also, it provided exercises of spatial reasoning and geometric transformation. Based on the interviews with students that many students of vocational school preferred the teacher to explain the material and gives examples or ask students to solve the mathematical problems with small group discussion. Moreover, vocational school students preferred worksheet that already provided the formula. In the developed worksheets, we presented some formulas, examples, and exercises that could be solved through discussions with classmates or small group discussions.
For example, in the worksheet (
In the worksheet (
In
The implementation of lesson plans and students’ worksheets aimed to determine the practicality and effectiveness of instructional package. The test of products was conducted at SMKN 2 Ngawi with 106 students. The learning activities were guided by lesson plans and worksheets which had been designed. We had provided the worksheets for each student. In the learning process, students were not asked to always sit in groups, but to discuss the provided problems on the worksheet with the guidance of teachers in the classroom. This part discussed the implementation of the instructional package in four meetings. The following are reviews of each meeting.
We applied developed worksheet four times during research. The first meeting was held in AE 3 class and AE 1 class. In general, learning ran, but it did not meet the expectation regarding the use of worksheets. For this condition, we tried to discuss this problem with teachers to find the solution. Then we tried applying the solution in BST 1 class. In the second meeting up to the fourth meeting, although not precisely similar to research design, learning using developed worksheets started to work. The topics during research are 1) translation for the first meeting, 2) reflection in the second meeting; 3) rotation for the third meeting; and 4) dilation for the fourth meeting. Spatial orientation, visualization, spatial perception and spatial relation can be built while learning all the topics except for mental rotation which can only be built upon rotation.
Generally, for the first meeting in three classes, students were not familiar with the developed worksheets, so it took quite a long time. During the learning, many students did not discuss with other students but trying to solve their own "Asah Kemampuan" activities. Many students still could not follow the learning using worksheets. Consequently, the exercise activities could not be implemented in the class and made as homework. Moreover, the teacher had no chance to ask the student to present their conclusions and reflection. However, it turned out that some students have written their conclusions on the worksheet.
At the second meetings in AE 3 and AE 1 classes, the learning activities had already started based on the plan, but there were still some unfulfilled activities such as solving exercise activities and teacher still appointed students to deliver their solution. In other class, students began to be active in the learning process, and some students bravely asked related problems in the worksheets. Then, students made illustrations by moving their hands to ease thinking about transformation. After that, students draw the transformationplane in the provided Cartesian plane.
Based on the evaluation from two classes, students wanted the teacher to give them explanation before they started working on the worksheet. That is why at the first meeting in the BST 1 class, the teacher tried to explain, and the learning process had started by the plan. Although some students were not enthusiastic with learning using worksheet, many students were willing to be actively involved in learning and started discussions with other students. The students were active in the discussion, but no student was submitting the worked problems. In this case, the teacher appointed some students. Later, several activities such as making reflections could not be carried out since time were spent in the activities of drawing the plane in the Cartesian field and making conclusions. At the second meeting, the teacher made the problem solving as part of drawing plane so that one group solved one problem only. The drawing plane made learning more efficient, and other activities could be accomplished. When the teacher went around, the students asked questions and showed the results of their solutions. Moreover, when the teacher appointed one of the students to deliver the results, he enthusiastically wrote the results on the board.
In the third and fourth meeting in three classes, several students asked the teacher about their answers. The students still preferred to be appointed when presenting their answers in front of the class. However, some students wanted to represent their group even if not appointed by the teacher. Even though many students were active in the learning process, there were still two students who seemed silent and didn’t follow the lesson. Moreover, at the fourth meeting, there were no students who respond to the other students' work presented on the whiteboard. Here is the sample of student’s work.
After the learning process, evaluation began by analyzing data on the practicality and effectiveness of instructional package. Data for practicality was collected from the observation of learning and practicality examination by the teacher and students. Based on


Lesson plan  33,5 
Student’s worksheet  37,5 
Learning implementation  26,5 







AE1  61,4  Practical 
AE 3  58,3  Practical 
BST  60,5  Practical 
The third practicality instrument is learning observation sheet. It is based on the activity steps in the lesson plan.














1  79  86  83  90  86  90 
2  100  93  88  86  97  93 
3  100  93  100  93  97  93 
4  100  97  100  97  100  100 
















Based on
Effectiveness is examined through spatial reasoning tests. The students were given spatial reasoning tests consisting of five items of multiplechoicequestions. Multiplechoicequestion is easier to use than essay since multiple choices focus on thinking and the distractor a student choice may give teacher diagnostic insight into students’ difficulties (Nitko & Brookhart, 2011) [







Highest score  100  100  100 
Lowest score  40  20  40 
Average score 



Total average 


Classical percentage  86%  78%  82% 
Total percentage 

Some students get the maximum score which reveals that the student was capable of all aspects of spatial reasoning. The average score of the AE 1 class was 78.9 with the percentage of completeness was 86%. The average score of the AE 3 class was 73.3 with the percentage of classical completeness was 78%, while the average of BST class was 78.8 with the percentage of completeness was 82%. Besides, the overall average of spatial reasoning ability was 72.3 with the percentage of spatial reasoning ability was 82%. Thus, the mathematics instructional package (lesson plan and worksheet) developed was effective concerning students' spatial reasoning because of the percentage of spatial reasoning ability reach X≥80%







Spatial orientation  26  31  27 
Spatial visualization  36  35  30 
Mental rotation  19  20  22 
Spatial relation  33  32  30 
Spatial perception  32  17  21 
In the test (fig. 9), 22 of 106 students chose A. When examining the test item, and the option A was not possible as the answer to the question. It was because the "cross" on the upper side became the center of rotation so that the "cross" side would remain in its original position. However, in fact, many students chose A. It was possible because students estimated by looking at the front side that contained the "star" image unchanged, while the top side containing "cross" rotated 90° in the clockwise direction.
The research found that students had difficulty distinguishing between abscissa and ordinate, square and rectangle in the Cartesian field, and the characteristic of the regular plane. After going through the learning using lesson plans and worksheets gradually, students were able to overcome these difficulties. The data also pointed out the improvement in students' thinking level. Without making calculations, students were able to describe plane displacement which indicated that the package supports students' spatial reasoning.
The findings were similar to Alattin (2016) [
In the worksheet, there were also student activities such as “Asah Kemampuan” or drawing activities to explore the ability of spatial reasoning so that students became excited, interested and enthusiastic to do activities in drawing the object of geometric transformation. The drawing/sketching and spatial painting activities guided by teachers are an effective way to improve spatial abilities and attract students' attention (Davis, 2015; Mohler & Miler, 2008) [
The research found that the mathematics instructional package developed based on van Hiele theory and oriented to spatial reasoning is practical and effective. The practicality refers to the fulfillment of practical criteria which was examined through three instruments, i.e., teacher's practicality sheet, student's practicality sheet and learning observation. The effectivity is perceived through spatial reasoning test which shows that the overall average of students’ spatial reasoning ability was 72.3 with the percentage of spatial reasoning ability was 82%. The package has several characteristics which support students’ spatial reasoning, i.e. learning activities using van Hiele learning phase which consist of identifying students' initial ability in the information phase, giving examples or practice of drawing geometry in the Cartesian field in the guided orientation phase, exploring students’ ability in conveying their ideas during explanation phase, completing the problems even without calculation in the free orientation phase, and identifying students’ whole knowledge after learning the topics in the integration phase. Also, the worksheet provides the Cartesian field to facilitate students in spatial thinking. It also gives additional information such as formulas and the steps to induce it.
The author declare that no competing interests exist.